Elliptic curves in moduli space of stable bundles

2010/11/19 by Xiaotao Sun, Sun, Xiaotao
Mathematics · #14H60 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1011.4482

openalex publication_date 2010/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be the moduli space of rank 2 stable bundles with fixed determinant of degree 1 on a smooth projective curve C of genus g≥ 2. When C is generic, we show that any elliptic curve on M has degree (respect to anti-canonical divisor -K_M) at least 6, and we give a complete classification for elliptic curves of degree 6. Moreover, if g>4, we show that any elliptic curve passing through the generic point of M has degree at least 12. We also formulate a conjecture for higher rank.

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