HIGHER RANK BRILL–NOETHER THEORY ON SECTIONS OF K3 SURFACES

DOI10.1142/S0129167X12500759zbMath1256.14032arXiv1102.0276OpenAlexW2963112180MaRDI QIDQ2909471

Angela Ortega, Gavril Farkas

Publication date: 30 August 2012

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1102.0276

zbMATH Keywords

Koszul cohomologyBrill-Noether theoryLazarsfeld-Mukai bundleMercat conjecture

Mathematics Subject Classification ID

Vector bundles on surfaces and higher-dimensional varieties, and their moduli (14J60) (K3) surfaces and Enriques surfaces (14J28) Vector bundles on curves and their moduli (14H60)

Related Items (12)

Counterexamples to Mercat's conjecture ⋮ An effective restriction theorem via wall-crossing and Mercat's conjecture ⋮ Higher rank Brill—Noether theory and coherent systems open questions ⋮ Scroll codes over curves of higher genus: reducible and superstable vector bundles ⋮ On bundles of rank 3 computing Clifford indices ⋮ Bundles of rank 3 on curves of Clifford index 3 ⋮ Generalized Lazarsfeld-Mukai bundles and a conjecture of Donagi and Morrison. ⋮ Severi varieties and Brill-Noether theory of curves on abelian surfaces ⋮ Lazarsfeld-Mukai bundles of rank 2 on a polarized \(K3\) surface of low genus ⋮ Curves on surfaces with trivial canonical bundle ⋮ On stability of tautological bundles and their total transforms ⋮ The Strong Maximal Rank conjecture and higher rank Brill–Noether theory

Cites Work

• Special divisors on curves on a K3 surface
• Linear systems on K3-sections
• Curves and symmetric spaces. II.
• Koszul cohomology and the geometry of projective varieties. Appendix: The nonvanishing of certain Koszul cohomology groups (by Mark Green and Robert Lazarsfeld)
• Brill-Noether-Petri without degenerations
• On the Wahl map of curves with Brill-Noether-Petri condition
• Projective degenerations of \(K3\) surfaces, Gaussian maps, and Fano threefolds
• The maximal rank conjecture and rank two Brill-Noether theory
• Further examples of stable bundles of rank 2 with 4 sections
• Clifford Indices for Vector Bundles on Curves
• STABLE BUNDLES OF RANK 2 WITH FOUR SECTIONS
• Smooth Curves on Projective $K3$ Surfaces
• CLIFFORD'S THEOREM AND HIGHER RANK VECTOR BUNDLES
• green's canonical syzygy conjecture for generic curves of odd genus

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