Extending Vector Bundles from Curves

2020/10/07 by Siddharth Mathur, Mathur, Siddharth
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.2010.03221

Section 2 completely rewritten, to appear in Mathematical Research Letters

arxiv created 2021/04/05 · arxiv updated 2021/04/06

Abstract

Given a curve in a (smooth) projective variety C ⊂ X, we show that a vector bundle V on C can be extended to a (μ-stable) vector bundle on X if rank(V) ≥ dim(X) and det(V) extends to X.

Related

• Stable extensions by line bundles
• Families of maximal subbundles of stable vector bundles on curves
• A stratification of the moduli space of vector bundles on curves
• On Poincare bundles of vector bundles on curves
• Extensions and rank-2 vector bundles on irreducible nodal curves