Rational curves and lines on the moduli space of stable bundles

2013/05/15 by Zhou, Mingshuo
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1305.3394

Abstract

Fix a smooth projetive curve \mathcal C of genus g≥ 2 and a line bundle L on C of degree d. Let M:= SU_C(r, L) be the moduli space of stable vector bundles on C of rank r and with fixed determinant L. We prove that any rational curve on M is a generalized Hecke curve. Furthermore, we study the lines on M, and prove that M is covered by the lines when (r, d)=r; for the case (r,d)(r,d)+1. Finally, we prove that there are no (1,0)-stable (resp., (0,1)-stable) bundles for g=2, r=2 and d is odd as an application.

Related

• Minimal rational curves in moduli spaces of stable bundles
• Small rational curves on the moduli space of stable bundles
• Remarks on minimal rational curves on moduli spaces of stable bundles
• Rationality of moduli spaces of stable bundles on curves over ℝ
• On vector bundles over moduli spaces trivial on Hecke curves