Stable maps of genus zero in the space of stable vector bundles on a curve

Abstract

Let [Formula: see text] be a smooth projective curve with genus [Formula: see text]. Let [Formula: see text] be the moduli space of stable rank two vector bundles on [Formula: see text] with a fixed determinant [Formula: see text] for [Formula: see text]. In this paper, as a generalization of Kiem and Castravet’s works, we study the stable maps in [Formula: see text] with genus [Formula: see text] and degree [Formula: see text]. Let [Formula: see text] be a natural closed subvariety of [Formula: see text] which parametrizes stable vector bundles with a fixed subbundle [Formula: see text] for a line bundle [Formula: see text] on [Formula: see text]. We describe the stable map space [Formula: see text]. It turns out that the space [Formula: see text] consists of two irreducible components. One of them parameterizes smooth rational cubic curves and the other parameterizes the union of line and smooth conics.