Rational families of vector bundles on curves, I

Abstract

Let C be a smooth complex projective curve of genus at least 2 and let M be the moduli space of rank 2, stable vector bundles on C, with fixed determinant of degree 1. For any k>1, we find two irreducible components of the space of rational curves of degree k on M. One component, which we call the nice component has the property that the general element is a very free curve if k is sufficiently large. The other component has the general element a free curve. Both components have the expected dimension and their maximal rationally connected fibration is the Jacobian of the curve C.

arXiv comment23 pages

References in corpus (4)

• The connectedness of the moduli space of maps to homogeneous spaces
• Abel-Jacobi maps associated to smooth cubic threefolds
• Rational curves on hypersurfaces of low degree
• Curves of small degree on cubic threefolds

Cited by in corpus (1)

• Twisted sheaves and the period-index problem