Publications
Prof. Dr. Frank-Olaf Schreyer
Preprints:
The variety of polar simplices II, arXiv:2304.00533 (2023), (with Joachim Jelisiejew and Kristian Ranestad) | |
Hyperelliptic curves and Ulrich sheaves on the complete intersection of two quadrics, arXiv:2212.07227 (2022) (with David Eisenbud) |
|
Marked Godeaux surfaces with special bicanonical fibers, arXiv:2201.12065 (2022) (with Isabel Stenger) |
|
Variety Membership Testing, Algebraic Natural Proofs, and Geometric Complexity Theory, arXiv: 1911.02534 (with M. Bläser, C. Ikenmeyer, V. Lysikov, A. Pandey) |
(Peer-reviewed) Articles:
72. |
An 8-dimensional family of simply connected Godeaux surfaces, Trans. of the American Mathematical Society 376 (05), 3419-3443 (with Isabel Stenger) |
71. |
Birational geometry and the canonical ring o a family of determinantal 3-folds, Rend. Ist. Mat. Univ. Trieste 54, Paper No. 9, 15 p. (2022) (with V. Lazić) |
70. |
Tate Resolutions and Maximal Cohen-Macaulay Approximations, Contemp. Math. 773, 35-47 (2021) (with D. Eisenbud) |
69. |
Unirational component of moduli spaces of genus 11 curves with several pencils of degree 6, Doc. Math. 26, 415-438 (2021) (with H. Keneshlou) |
68. |
Horrocks splitting on Segre-Veronese varieties, Math. Z. 300, No. 2, 1351-1358 (2022). |
67. |
Quadratic complete intersections, J. Algebra 571, 15-31 (2021) (with D. Eisenbud and I. Peeva) |
66. | A version of Green's conjecture in positive characteristic, Exp. Math. 30,no. 4, 475-480 (2021) (with C. Bopp) |
65. | An explicit matrix factorization of cubic hypersurfaces of small dimension, Journal of Pure and Applied Algebra 224 (2020), no. 8 (with Y. Kim) |
64. | Singular value decomposition of complexes, SIAM J. Appl. Algebra Geom. 3 (2019), no. 3, 507–522. (with D.A. Brake, J.D. Hauenstein, A.J. Sommese and M.E. Stillman) |
63. | Non-commutative CI operators. Proc. Amer. Math. Soc. 147 (2019), no. 7, 2857–2861. (with D. Eisenbud and I. Peeva) |
62. | Equations and Syzygies of K3 Carpets and Unions of Scrolls, Acta Math. Vietnam. 44 (2019), no. 1, 3–29. (with D. Eisenbud) |
61. |
Tor as a module over an exterior algebra, J. Eur. Math. Soc. (JEMS) 21 (2019), no. 3, 873–896. (with D. Eisenbud and I. Peeva) |
60. |
Matrix factorizations and curves in P4, Doc. Math. 23 (2018), 1895–1924. (with F. Tanturri) |
59. | Ulrich Complexity, Differential Geom. Appl. 55 (2017), 128–145. (with M. Bläser and D. Eisenbud) |
58. | Unirationality of the Hurwitz space H9,8, Arch. Math. (Basel) 109, 511–519 (2017) (with H. Damadi) |
57. | Refined Algorithms to Compute Syzygies, Journal of Symbolic Computation, 74 (2016), 302-327 (with B. Eröcal, O. Motsak and A. Steenpass). |
56. |
Syzygies, finite length modules, and random curves, Commutative algebra and noncommutative algebraic geometry. Vol. I, 25–52, Math. Sci. Res. Inst. Publ., 67, Cambridge Univ. Press, New York, 2015. (with C. Berkesch). |
55. | Matrix factorizations and families of curves of genus 15, Algebraic Geometry 2 (2015), no. 4, 489-507. |
54. | Twenty Points in P^3, in C. Hacon, M. Mustaţă, M. Popa (eds): Recent Advances in Algebraic Geometry, 180-199, Cambridge (2015) (with D. Eisenbud and R. Hartshorne). |
53. | Tate Resolutions for Products of Projective Spaces, Acta Math. Vietnam. 40 (2015), no. 1, 5–36. (with D. Eisenbud and D. Erman). |
52. | Minimal Free Resolutions of the $G$-parking Function Ideal and the Toppling Ideal, Trans. Amer. Math. Soc. 367 (2015), no. 4, 2853–2874. (with M. Manjunath and J. Wilmes). |
51. | Computational aspects of gonal maps and radical parametrization of curves, Appl. Algebra Engrg. Comm. Comput. 24 (2013), no. 5, 313–341. (with J. Schicho and M. Weimann). |
50. | Syzygies of torsion bundles and the geometry of the level l modular variety over Mg, Inventiones Mathematicae 194 (2013), 73-118 (with A. Chiodo, D. Eisenbud and G. Farkas). |
49. | Computer aided unirationality proofs for moduli spaces, Handbook of Moduli, Volume III (2013), 257-280. |
48. | The Variety of Polar Simplices, Doc. Math. 18 (2013) 469-505 (with K. Ranestad). |
47. | Filtering free resolutions, Compos. Math. 149 (2013), no. 5, 754-772 (with D. Eisenbud and D. Erman). |
46. | The Banks of the Cohomology River, Kyoto J. Math. 53 (2013), no. 1, 131-144 (with David Eisenbud). |
45. | A remark to a conjecture of Paranjape and Ramanan. Geometry and arithmetic, 113-123, EMS Ser. Congr. Rep., Eur. Math. Soc., Zürich, 2012 (with F. Eusen). |
44. | ACM Curves of Small Degree and Cubic Threefolds, Appendix to the paper: Stable Ulrich Bundles by M. Casanellas and R. Hartshorne, Internat. J. Math. 23 (2012), no. 8, 1250083, 50 pp. (with Florian Geiß) |
43. | On the rank of a symmetric form, J. Algebra 346 (2011), 340-342 (with K. Ranestad). |
42. | Boij-Söderberg Theory. Combinatorial Aspects of Commutative Algebra and Algebraic Geometry, Abel Symposium 2009, 35-48, Springer Verlag 2011 (with David Eisenbud). |
41. | Betti Numbers of Syzygies and Cohomology of Coherent Sheaves, Proceedings of the ICM, Hyderabad 2010, vol. 2, 585-602 (with David Eisenbud). |
40. | Cohomology of coherent sheaves and series of supernatural bundles, J. Eur. Math. Soc. (JEMS) 12 (2010), no. 3, 703-722 (with David Eisenbud). |
39. | A family of exceptional Stewart-Gough mechanisms of genus 7, Interactions of classical and numerical algebraic geometry, 221-234, Contemp. Math. 496, Amer. Math. Soc., Providence, RI, 2009 (with Florian Geiß). |
38. | Betti Numbers of Graded Modules and Cohomology of Vector Bundles, J. Amer. Math. Soc. 22 (2009), no.3, 859-888 (with David Eisenbud). |
37. | Relative Beilinson Monad and Direct Image for Families of Coherent Sheaves, Trans. Amer. Math. Soc. 360 (2008), no. 10, 5367-5396 (with D. Eisenbud). |
36. | Exterior algebra methods for the construction of rational surfaces in the projective fourspace, London Math. Soc. Lecture Note Ser., 324, Cambridge Univ. Press, Cambridge, 2006 (with H. Abo). |
35. | A Quick and Dirty Irreducibility Test for Multivariate Polynomials over F_q, Experiment. Math. 14 (2005), no. 4, 415-422. (with H.-C. Graf v. Bothmer) |
34. | Some topics in Computational Algebraic Geometry, in C. Musili (ed): Advances in Algebra and Geometry (University of Hyderabad Conference 2001) 263-278, Hindustan Book Agency (India), New Delhi 2002. |
33. | Real Fano 3-folds of type V22, in A. Conte et al. (eds): Proceedings of the Fano Conference, Torino 2002 (with J. Kollár). |
32. | Computational Algebraic Geometry Today, in C. Ciliberto et al. (eds): Application of Algebraic Geometry to Coding Theory, Physics and Computation, 65-119, Kluwer 2001 (with W. Decker). |
31. | Resultants and Chow forms via exterior syzygies, J. Amer. Math. Soc. 16 (2003), 537-579 (with D. Eisenbud), Appendix by Jerzy Weyman . |
30. | Exterior algebra methods for the minimal resolution conjecture, Duke Math. J. 112 (2002), 379-395 (with D. Eisenbud, S. Popescu and C. Walter). |
29. | Needles in haystack: special varieties via small fields, in: D. Eisenbud, D. Grayson, M. Stillman, B. Sturmfels (eds.): Mathematical computations with Macaulay 2, 251-279, Springer (2001) (with F. Tonoli). |
28. | Sheaf cohomology and resolutions over the exterior algebra, Trans. Amer. Math. Soc. 355 (2003), 4397-4426, (with D. Eisenbud and G. Fløystad). |
27. | Canonical projections of irregular algebraic surfaces, in M. Beltrametti et. al. (eds.): Algebraic Geometry. A Volume in Memory of Paolo Francia, 79--116, de Gruyter Berlin 2002, (with F. Catanese). |
26. | Geometry and algebra of prime Fano 3-folds of genus 12, Compositio Math. 127 (2001), 297-319. |
25. | Moduli of (1,7)-polarized abelian surfaces via syzygies, Math. Nachr. 226 (2001), 177-203 (with N. Manolache). |
24. | Non-general Type Surfaces in P4: Some remarks on bounds and constructions, J. Symbolic Computation 29 (2000), 545--585 (with W. Decker). |
23. | Varieties of sums of powers, J. reine angew. Math. 525 (2000), 147-182 (with K. Ranestad). |
22. | Generating a noetherian normalization of the invariant ring of a finite group. J. of Symbolic Computation 25 (1998), 1-5 (with W. Decker and A.E. Heydtmann). |
21. | Fragen zum Mathematikstudium, ca. 19 Seiten in: Studienführer Mathematik der Universität Bayreuth. Mathematisches Institut der Universität Bayreuth, 1997, in Druck und in elektronischer Version. |
20. | Small fields in constructive algebraic geometry. In: M. Maruyama, editor: Moduli of vector bundles, Marcel Dekker Inc., New York 1996, 221-228. |
19. | Classification of conic bundles in P5. Annali della Scuola Normale Superiore di Pisa 23 (1996), 69-97 (with R. Braun, G. Ottaviani and M. Schneider). |
18. | Boundedness for non-general type 3-folds in P5. In: Complex Analysis and Geometry, edited by V. Ancona and A. Silva, Plenum Press (1993), 311-338 (with R. Braun, G. Ottaviani and M. Schneider). |
17. | Construction of surfaces in P4. J. Alg. Geom. 2 (1993), 185-237 (with W. Decker and L. Ein). |
16. | Geometry of the Horrocks bundle on P5. In: Complex projective geometry, London Math. Soc. Lecture Note Series 179 (1992), 128-148 (with W. Decker and N. Manolache). |
15. | Cremona transformations and syzygies. Math. Z. 209 (1992), 419-443 (with K. Hulek and S. Katz). |
14. | A standard basis approach to syzygies of canonical curves. J. reine angew. Math. 421 (1991), 83-123. |
13. | Rank 2 vector bundles on P4 with c1 odd and contact curves. Math. Z. 205 (1990), 123-136 (with W. Decker and M.S. Narasimhan). |
12. | The Clifford dimension of a projective curve. Compositio Math. 72 (1989), 173-204 (with D. Eisenbud, H. Lange and G. Martens). |
11. | Certain Weierstrass points occur at most once. In: Geometry and complex analysis, Proceedings Patzcuaro 1987, Springer Lecture Notes 1414, 162-168. |
10. | Green's conjecture for the general p-gonal curve of large genus. In: Algebraic curves and projective geometry, Proceedings Trento 1988, Springer Lecture Notes 1389, 254--260. |
9. | A Torelli theorem for osculating cones to the theta divisor. Compositio Math. 67 (1988), 343-353 (with G. Kempf). |
8. | Pullbacks of the Horrocks-Mumford bundle. J. reine angew. Math. 382 (1987), 215-220 (with W. Decker). |
7. | Finite and countable CM-representation type. In: Singularities, Representation of Algebras, and Vector Bundles, Proceedings Lambrecht 1985, Springer Lecture Notes 1273, 9-34. |
6. | Cohen-Macaulay modules on hypersurface singularities II. Invent. math. 88 (1987), 165-182 (with R.-O. Buchweitz and G.-M. Greuel). |
5. | On the uniqueness of the Horrocks-Mumford bundle. Math. Ann. 273 (1986), 415-443 (with W. Decker). |
4. | Syzygies and line bundles of trigonal curves, Abh. Math. Sem. Hamburg 56 (1986), 169-189 (with G. Martens). |
3. | Syzygies of canonical curves and special linear series. Math. Ann. 275 (1986), 105--137. |
2. | The Moduli of Curves is Stably Rational for g <= 6. Duke Math. J. 5 (1984), 239-242 (with J. Kollár). |
1. | Resolutions of Cohen-Macaulay Algebras. Math. Ann. 257 (1981), 85-98 (with D. Eisenbud and O. Riemenschneider). |
Publications
Christian Bopp
2. | Resolutions of general canonical curves on rational normal scrolls, Archiv der Mathematik, 2015, DOI: 10.1007/s00013-015-0794-x (with M. Hoff) |
1. | Syzygies of 5-gonal Canonical Curves, Doc. Math. 20 (2015), 1055-1069. |
Publications
Michael Hoff
5. | New examples of rational Gushel-Mukai fourfolds, Mathematische Zeitschrift, electronically published on February 27,2020, DOI: 10.1007/s00209-020-02498-5 (to appear in print) (with G. Staglianò) |
4. | Focal schemes to families of secant spaces to canonical curves, Algorithmic and experimental methods in algebra, geometry, and number theory, 387-401 (2017), DOI: 10.1007/978-3-319-70566-8 |
3. | Tangent cones to generalised theta divisors and generic injectivity of the theta map. Compositio Mathematica, 153(12), 2643-2657 (2017), DOI:10.1112/S0010437X17007539 (with G. H. Hitching) |
2. | Resolutions of general canonical curves on rational normal scrolls, Archiv der Mathematik (Basel) 105 (2015), no. 3, 239-249, DOI: 10.1007/s00013-015-0794-x (with C. Bopp) |
1. | The osculating cone to special Brill-Noether loci, Collectanea Mathematica 66 (2015), no. 3, 387-403, DOI:10.1007/s13348-015-0146-y (with U. Mayer) |
Publications
Dr. Fabio Tanturri
2. | Degeneracy loci of twisted differential forms and linear line complexes. To appear in Arch. Math.. |
1. | On the Hilbert scheme of degeneracy loci of twisted differential forms. To appear in Trans. Amer. Math. Soc.. |
Publications
Dr. Florian Geiß
3. | The unirationality of Hurwitz spaces of 6-gonal curves of small genus , Doc. Math. 17 (2012), 627-640. |
2. | ACM Curves of Small Degree and Cubic Threefolds, Appendix to the paper: Stable Ulrich Bundles by M. Casanellas and R. Hartshorne, Internat. J. Math. 23 (2012), no. 8, 1250083, 50 pp. (with Frank-Olaf Schreyer). |
1. | A family of exceptional Stewart-Gough mechanisms of genus 7. , Interactions of classical and numerical algebraic geometry, 221-234, Contemp. Math. 496, Amer. Math. Soc., Providence, RI, 2009 (with Frank-Olaf Schreyer). |
Publications
Dr. Oliver Labs
14. | Nullstellen von Polynomen in 2d und 3d - virtuell und real, Beiträge zum Mathematikunterricht 2012. |
13. | Nullstellen und Diskriminanten von Polynomen . Mit GeoGebra mehr Mathematik verstehen (Hrsg: R. Kaenders, R. Schmidt), Vieweg, 2011. |
12. | Terme in Bildern, Tagungsband des GDM-Arbeitskreises Geometrie (2011). |
11. | Algebraic Expansions: Broadening the Scope of Architectural Design through Algebraic Surfaces. Computational Design Modeling: Proceedings of the Design Modeling Symposium Berlin 2011. Springer Berlin Heidelberg, 2011. 8-16, (with Günter Barczik, Daniel Lordick). |
10. | Erweitertes geometrisches und skulpturales Gestaltungsvokabular für Architektur durch algebraische Flächen. Ästhetische Geometrie-Geometrische Ästhetik, Tagungsband der 6. Tagung der Deutschen Gesellschaft für Geometrie und Grafik (DGfGG), Herzogenrath : Shaker, 2010, ISBN 978-3-8322-9701-5, 46-51, (with Günter Barczik, Daniel Lordick). |
9. | Perplexing Beauty: The Aesthetics of Algebraic Geometry in Architecture. Proceedings of the 21st Biennial congress of the International Association of Empirical Aesthetics in Dresden (IAEA) "Aesthetics+ Design". 25.-28. August 2010, (with Günter Barczik, Daniel Lordick). |
8. | Algebraic Geometry in Architectural Design, to appear in eCAADe 2009, (with Günter Barczik, Daniel Lordick). |
7. | Surfaces with Many Solitary Points , Geom. Dedicata Vol. 141. 2009, 123-134, (with Erwan Brugallé). |
6. | A List of Challenges for Real Algebraic Plane Curve Visualization Software , Nonlinear Computational Geometry, IMA Volume 151, 137-164 (2009). |
5. | Real Line Arrangements and Surfaces with Many Real Nodes , Geometric Modeling and Algebraic Geometry (2008), 47-54, (with S. Breske and D. van Straten). |
4. | The Casas-Alvero conjecture for infinitely many degrees , J. Algebra, Vol. 316, No 1, 224-230, (with Hans-Christian Graf von Bothmer, Josef Schicho, Christiaan van de Woestijne). |
3. | Dessins d'Enfants and Hypersurfaces with Many Aj-Singularities , J. Lond. Math.Soc. (2), Vol. 74, 607-622 (2006) |
2. | A Septic with 99 real Nodes , Rend. Sem. Mat. Univ. Pad., Vol. 116, 299-313 (2006) |
1. | Illustrating the Classification of Real Cubic Surfaces , Algebraic Geometry and Geometric Modelling (2006), 119-134, (with S. Holzer). |
Publications
Dr. Madhusudan Manjunath
1. | Minimal Free Resolutions of the $G$-parking Function Ideal and the Toppling Ideal , to appear in Transactions of the American Mathematical Society (with F.-O. Schreyer and J. Wilmes) |