Syzygies of torsion bundles and the geometry of the level \(\ell \) modular variety over \(\overline{\mathcal{M}}_{g}\)

DOI10.1007/s00222-012-0441-0zbMath1284.14006arXiv1205.0661OpenAlexW1512143977MaRDI QIDQ378057

Gavril Farkas, Alessandro Chiodo, David Eisenbud, Frank-Olaf Schreyer

Publication date: 11 November 2013

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.0661

zbMATH Keywords

minimal resolution of paracanonical curvesmoduli of (twisted) level curvesPrym-Green conjecture

Mathematics Subject Classification ID

Families, moduli of curves (algebraic) (14H10) Families, moduli of curves (analytic) (14H15) Algebraic geometry (14-XX)

Related Items (18)

Brill-Noether theory for cyclic covers ⋮ The generic Green-Lazarsfeld secant conjecture ⋮ Views on level \(\ell\) curves, \(K3\) surfaces and Fano threefolds ⋮ Minimal resolutions, Chow forms and Ulrich bundles on \(K3\) surfaces ⋮ The nonabelian Brill-Noether divisor on \(\overline{\mathcal{M}}_{13}\) and the Kodaira dimension of \(\overline{\mathcal{R}}_{13}\) ⋮ Refined algorithms to compute syzygies ⋮ Progress on Syzygies of Algebraic Curves ⋮ On the first Gaussian map for Prym-canonical line bundles ⋮ Most odd degree hyperelliptic curves have only one rational point ⋮ Level structures on abelian varieties, Kodaira dimensions, and Lang's conjecture ⋮ Singularities of moduli of curves with a universal root ⋮ Singularities of the moduli space of level curves ⋮ The resolution of paracanonical curves of odd genus ⋮ A characterization of bielliptic curves via syzygy schemes ⋮ Combinatorial enumeration of cyclic covers of P1 ⋮ Twists of Mukai bundles and the geometry of the level $3$ modular variety over $\overline {\mathcal {M}}_{8}$ ⋮ Birational geometry of moduli of curves with an \(S_3\)-cover ⋮ Moduli of \(G\)-covers of curves: geometry and singularities

Uses Software

• KoszulDivisorOnPic14M8
• ParanjapeRamananQuestion.m2

Cites Work

• Unnamed Item
• Unnamed Item
• The classification of universal Jacobians over the moduli space of curves
• Moduli of theta-characteristics via Nikulin surfaces
• Singularities of the moduli space of level curves
• The rationality of the moduli space of genus-4 curves endowed with an order-3 subgroup of their Jacobian
• Koszul cohomology and the geometry of projective varieties. Appendix: The nonvanishing of certain Koszul cohomology groups (by Mark Green and Robert Lazarsfeld)
• Generic syzygy schemes
• Stable twisted curves and their \(r\)-spin structures
• The Kodaira dimension of the moduli space of Prym varieties
• The Kodaira dimension of the moduli space of curves of genus \(\geq 23\)
• On the Kodaira dimension of the moduli space of curves
• GEOMETRY OF THE MODULI OF HIGHER SPIN CURVES
• Compactifying the space of stable maps
• Fibrés de rang 2 sur une courbe, fibré déterminant et fonctions thêta
• The Rationality of Certain Moduli Spaces of Curves of Genus 3
• A standard basis approach to syzygies of canonical curves.
• The unirationality of the moduli spaces of curves of genus 14 or lower
• Moduli of roots of line bundles on curves
• Towards an enumerative geometry of the moduli space of twisted curves and rth roots
• Koszul divisors on moduli spaces of curves
• Twisted Bundles and Admissible Covers
• Divisors on and the minimal resolution conjecture for points on canonical curves
• A remark on a conjecture of Paranjape and Ramanan
• green's canonical syzygy conjecture for generic curves of odd genus
• The Picard group of the moduli of higher spin curves

This page was built for publication: Syzygies of torsion bundles and the geometry of the level \(\ell \) modular variety over \(\overline{\mathcal{M}}_{g}\)