**Publications**

Prof. Dr. Frank-Olaf Schreyer

Preprints:

Birational geometry and the canonical ring o a family of determinantal 3-folds, arXiv: 1911.10954 (with V. Lazić) |

Variety Membership Testing, Algebraic Natural Proofs, and Geometric Complexity Theory, arXiv: 1911.02534 (with M. Bläser, C. Ikenmeyer, V. Lysikov, A. Pandey) |

Tate Resolutions and Maximal Cohen-Macaulay Approximations, arXiv: 1906.06398 (with D. Eisenbud) |

Tate Resolutions on Products of Projective Spaces: Cohomology and Direct Image Complexes, arXiv: 1905.10230 (with D. Eisenbud and D. Erman) |

Unirational component of moduli spaces of genus 11 curves with several pencils of degree 6, arXiv:1903.00254 (with H. Keneshlou) |

Horrocks splitting on Segre-Veronese varieties, arXiv: 1707.00249 |

(Peer-reviewed) Articles:

67. |
Quadratic complete intersections, to appear in Journal of Algebra (2019) (with D. Eisenbud and I. Peeva) |

66. | A version of Green's conjecture in positive characteristic, to appear in Experimental Mathematics (2019) (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, |

60. |
Matrix factorizations and curves in P |

59. | Ulrich Complexity, Differential Geom. Appl. 55 (2017), 128–145. (with M. Bläser and D. Eisenbud) |

58. | Unirationality of the Hurwitz space H_{9,8}, 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, |

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 V_{22}, 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 P^{4}: 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 P^{5}. 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 P^{5}. 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 P^{4}. J. Alg. Geom. 2 (1993), 185-237 (with W. Decker and L. Ein). |

16. | Geometry of the Horrocks bundle on P^{5}. 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 P^{4} with c_{1} 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). |