Prof. Dr. Frank-Olaf Schreyer


  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:


An 8-dimensional family of simply connected Godeaux surfaces, Trans. of the American Mathematical Society 376 (05), 3419-3443 (with Isabel Stenger)


Birational geometry and the canonical ring o a family of determinantal 3-foldsRend. Ist. Mat. Univ. Trieste 54, Paper No. 9, 15 p. (2022) (with V. Lazić)


Tate Resolutions and Maximal Cohen-Macaulay ApproximationsContemp. Math. 773, 35-47 (2021) (with D. Eisenbud)


Unirational component of moduli spaces of genus 11 curves with several pencils of degree 6, Doc. Math. 26, 415-438 (2021) (with H. Keneshlou)


Horrocks splitting on Segre-Veronese varieties, Math. Z. 300, No. 2, 1351-1358 (2022).


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)

Tor as a module over an exterior algebraJ. Eur. Math. Soc. (JEMS) 21 (2019), no. 3, 873–896. (with D. Eisenbud and I. Peeva)


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 H9,8Arch. 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).

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).


 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 CurvesDoc. Math. 20 (2015), 1055-1069.


 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 scrollsArchiv 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)


 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..


 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).


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).


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)
© AG Schreyer