A Version of Green’s Conjecture in Positive Characteristic

References

• [Aprodu 05] M. Aprodu. “Remarks on Syzygies of d-Gonal Curves.” Math. Res. Lett. 12:2–3 (2005), 387–400.
   Web of Science ®Google Scholar
• [Aprodu and Farkas 11] M. Aprodu and G. Farkas. “Green’s Conjecture for Curves on Arbitrary K3 Surfaces.” Compos. Math. 147:3 (2011), 839–851.
   Web of Science ®Google Scholar
• [Arbarello and Cornalba 83] E. Arbarello and M. Cornalba. “A Few Remarks About the Variety of Irreducible Plane Curves of Given Degree and Genus.” Ann. Sci. École Norm. Sup. 16:3 (1983), 467–488.
   Web of Science ®Google Scholar
• [Bopp 17] C. Bopp. “Canonical Curves, Scrolls and K3 Surfaces.” Thesis (Ph.D.), Saarland University (https://publikationen.sulb.uni-saarland.de/handle/20.500.11880/26917), 2017.
   Google Scholar
• [Bothmer and Schreyer 05] H.-C. G. V. Bothmer and F.-O. Schreyer. “A Quick and Dirty Irreducibility Test for Multivariate Polynomials Over Fq.” Experiment. Math. 14:4 (2005), 415–422.
   Web of Science ®Google Scholar
• [Bopp and Schreyer 17] C. Bopp and F.-O. Schreyer. “Random Curves Over Very Small Finite Fields, A Package for Macaulay2.” (https://faculty.math.illinois.edu/Macaulay2/Packages), 2017.
   Google Scholar
• [Bothmer et al. 11] H.-C. G. V. Bothmer, F. Geiß, and F.-O. Schreyer. “Random Curves, A Package for Macaulay2.” (http://www.math.uiuc.edu/Macaulay2/Packages/), 2011.
   Google Scholar
• [Chang and Ran 84] M. C. Chang and Z. Ran. “Unirationality of the Moduli Spaces of Curves of Genus 11, 13 (and 12).” Invent. Math. 76:1 (1984), 41–54.
   Web of Science ®Google Scholar
• [Eisenbud and Harris 87] D. Eisenbud and J. Harris. “On Varieties of Minimal Degree (A Centennial Account).” In Algebraic Geometry, Bowdoin, 1985 (Brunswick, Maine, 1985), Vol. 46 of Proc. Sympos. Pure Math., pp. 3–13. Providence, RI: American Mathematical Society, 1987.
   Google Scholar
• [Eisenbud and Schreyer 18] D. Eisenbud and F.-O. Schreyer. “Equations and Syzygies of K3 Carpets and Unions of Scrolls. (arXiv: 1804.08011)”, 2018.
   Google Scholar
• [Eröcal et al. 16] B. Eröcal, O. Motsak, F.-O. Schreyer, and A. Steenpaß. “Refined Algorithms to Compute Syzygies.” J. Symbolic Comput. 74 (2016), 308–327.
   Web of Science ®Google Scholar
• [Farkas and Kemeny 16] G. Farkas and M. Kemeny. “Linear Syzygies on Curves with Prescribed Gonality.” https://arxiv.org/abs/1610.04424, 2016.
   Google Scholar
• [Grayson and Stillman] D. R. Grayson and M. E. Stillman. “Macaulay2, A Software System for Research in Algebraic Geometry.” http://www.math.uiuc.edu/Macaulay2.
   Google Scholar
• [Green 84] M. L. Green. “Koszul Cohomology and the Geometry of Projective Varieties.” J. Differ. Geom. 19:1 (1984), 125–171.
   Web of Science ®Google Scholar
• [Mukai 10] S. Mukai. “Curves and Symmetric Spaces, II.” Ann. of Math. 172:3 (2010), 1539–1558.
   Web of Science ®Google Scholar
• [Sagraloff 06] M. Sagraloff. “Special Linear Series and Syzygies of Canonical Curves of Genus 9.” arXiv:math/0605758, 2006.
   Google Scholar
• [Schreyer 86] F.-O. Schreyer. “Syzygies of Canonical Curves and Special Linear Series.” Math. Ann. 275 (1986), 105–137.
   Web of Science ®Google Scholar
• [Schreyer 03] F.-O. Schreyer. “Some Topics in Computational Algebraic Geometry.” In Advances in Algebra and Geometry (Hyderabad, 2001), pp. 263–278. New Delhi: Hindustan Book Agency, 2003.
   Google Scholar
• [Schreyer 13a] F.-O. Schreyer. “Computer aided Unirationality Proofs of Moduli Spaces.” In Handbook of Moduli. Vol. III: Vol. 26 of Advanced Lectures in Mathematics (ALM), pp. 257–280. Somerville, MA: Int. Press, 2013.
   Google Scholar
• [Schreyer 13b] F.-O. Schreyer. “MatFac15, a Package for Macaulay2.” http://www.math.uni-sb.de/ag/schreyer/index.php/computeralgebra, 2013.
   Google Scholar
• [Schreyer 15] F.-O. Schreyer. “Matrix Factorizations and Families of Curves of Genus 15.” Algebr. Geom. 2:4 (2015), 489–507.
   Web of Science ®Google Scholar
• [Sernesi 81] E. Sernesi. “Unirationality of the Variety of Moduli of Curves of Genus Twelve.” Ann. Scuola Norm. Sup. Pisa Cl. Sci. 8:3 (1981), 405–439.
   Google Scholar
• [Schreyer and Tonoli 02] F.-O. Schreyer and F. Tonoli. “Needles in a Haystack: Special Varieties via Small Fields.” In Computations in Algebraic Geometry with Macaulay 2, Vol. 8 of Algorithms Comput. Math., pp. 251–279. Berlin: Springer, 2002.
   Google Scholar
• [Schicho et al. 13] J. Schicho, F.-O. Schreyer, and M. Weimann. “Computational Aspects of Gonal Maps and Radical Parametrization of Curves.” Appl. Algebra Eng. Comm. Comput. 24:5 (2013), 313–341.
   Web of Science ®Google Scholar
• [Verra 05] A. Verra. “The Unirationality of the Moduli Spaces of Curves of Genus 14 or Lower.” Compos. Math. 141:6 (2005), 1425–1444.
   Web of Science ®Google Scholar
• [Voisin 02] C. Voisin. “Green’s Generic Syzygy Conjecture for Curves of Even Genus Lying on a K3 Surface.” J. Eur. Math. Soc. (JEMS) 4:4 (2002), 363–404.
   Web of Science ®Google Scholar
• [Voisin 05] C. Voisin. “Green’s Canonical Syzygy Conjecture for Generic Curves of Odd Genus.” Compos. Math. 141 (2005), 1163–1190.
   Web of Science ®Google Scholar