On The Cohomology of N_C(-2) in Positive Characteristic

2023/08/26 by Eric Larson, Larson, Eric · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Geometry and complex manifolds #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2308.13756

Abstract

Let C ⊂ ℙ³ be a general Brill--Noether curve. A classical problem is to determine when H⁰(N_C(-2)) = 0, which controls the quadric section of C. So far this problem has only been solved in characteristic zero, in which case H⁰(N_C(-2)) = 0 with finitely many exceptions. In this note, we extend these results to positive characteristic, uncovering a wealth of new exceptions in characteristic 2.

Cited by

• Stability of normal bundles of Brill--Noether curves in ℙ⁴

Related

• Non-emptiness of Brill-Noether loci in M(2,K)
• Non-emptiness of Brill-Noether loci in M(2,L)
• Non-abelian cohomology of universal curves in positive characteristic
• Betti numbers of Brill-Noether varieties on a general curve
• Brill-Noether loci and strata of differentials