Families of vector bundles and linear systems of theta divisors

Abstract

Let [Formula: see text] be a smooth complex projective curve of genus [Formula: see text] and let [Formula: see text] be a point. From Hecke correspondence, any stable bundle on [Formula: see text] of rank [Formula: see text] and determinant [Formula: see text] defines a rational family of semistable vector bundles on [Formula: see text] of rank [Formula: see text] and trivial determinant. In this paper, we study linear systems of theta divisors associated to these families.

Genus 2 curves and generalized theta divisors

“…where G γ is actually a vector bundle which is obtained by the elementary tranformation of F at p defined by γ. Finally, G γ 1 ≃ G γ 2 if and only if [γ 1 ] = [γ 2 ] in P(Hom(F p , C)), see [Mar82] and [Bri17].…”

Nodal curves and polarizations with good properties

“…These spaces are interesting by themselves as higher dimensional varieties but also for important related constructions: just to mention some, one can consider higher-rank Brill-Noether theory, Theta divisors and Theta functions and the moduli spaces of coherent systems. For surveys on these topics see, for example [3,6,7]; for some results by the authors see [5,8,[11][12][13][14]. When the curve is singular, these spaces are not in general complete.…”