Advanced Computational Algebraic Geometry


First lecture on 28/4. First exercise session on 8/5.


Tentative topics of this course are

  • coherent sheaves cohomology
  • Boij-Söderberg theory
  • Tate resolutions on product of projective spaces
  • unirationality proofs of moduli spaces 
  • random curves
  • Chow forms and resultants


Eisenbud et al. (Eds) Computations in Algebraic Geometry with Macaulay2  Springer Verlag  2002
D. Eisenbud, G. Floystad, F.-O. Schreyer Sheaf cohomology and resolutions over the exterior algebra  Trans. Amer. Math. Soc.  2003
D. Eisenbud,  F.-O. Schreyer Resultants and Chow forms via exterior syzygies  J. Amer. Math. Soc.  2003
D. Eisenbud,  F.-O. Schreyer Betti Numbers of Syzygies and Cohomology of Coherent Sheaves  Proceedings of the ICM  2010
D. Eisenbud,  F.-O. Schreyer Boij-Söderberg Theory. Combinatorial Aspects of Commutative Algebra and Algebraic Geometry  Springer Verlag  2011
F.-O. Schreyer Computer aided unirationality proofs for moduli spaces  in Handbook of Moduli, Volume III  2013


  • 2 hours lectures, 2 hours excercise session
  • 6 Credit points
  • 30h hours total time for lectures
  • 30h hours total time for excercises
  • 120h hours total time for self-study


The lectures take place on Mondays, 2-4 pm, in room HS IV, building E2 4.


Regular attendance to exercise sessions. Written or oral exam at the end of term.


Exercise sessions take place on Thursdays, 10-12 am, in Seminarraum 5 (011) . In the exercise sessions we plan to discuss together about questions and problems arising from lectures. A list of suggested topics will be sent per e-mail every week after Monday's lecture; a summarizing list could be downloaded here.

Contact us

Fabio Tanturri
Zi. 429, Geb. E2 4
D-66123 Saarbrücken
Tel. +49(0)681/302-2430
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© AG Schreyer