Syzygies of torsion bundles and the geometry of the level a modular variety over

• 成果类型: Article
• 署名作者: Chiodo, Alessandro; Eisenbud, David; Farkas, Gavril; Schreyer, Frank-Olaf
• 署名单位: Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); University of California System; University of California Berkeley; Humboldt University of Berlin; Saarland University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-012-0441-0
• 发表日期: 2013
• 页码: 73-118
• 关键词: kodaira dimension; twisted curves; SPACE; conjecture; divisors

摘要

We formulate, and in some cases prove, three statements concerning the purity or, more generally, the naturality of the resolution of various modules one can attach to a generic curve of genus g and a torsion point of a in its Jacobian. These statements can be viewed an analogues of Green's Conjecture and we verify them computationally for bounded genus. We then compute the cohomology class of the corresponding non-vanishing locus in the moduli space of twisted level a curves of genus g and use this to derive results about the birational geometry of . For instance, we prove that is a variety of general type when g > 11 and the Kodaira dimension of is greater than or equal to 19. In the last section we explain probabilistically the unexpected failure of the Prym-Green conjecture in genus 8 and level 2.