Some stable vector bundles with reducible theta divisors

2002/09/09 by Arnaud Beauville, Beauville, Arnaud
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.math/0209089

7 pages, Plain TeX

arxiv created 2002/09/09 · openalex publication_date 2002/09/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let C be a curve of genus g and L a line bundle of degree 2g on C . Let M be the kernel of the evaluation map from the trivial bundle with fibre H⁰(C,L) into L . We show that when L is general enough, the rank g bundle M and its exterior powers are stable and admit a reducible theta divisor.

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