In this paper we investigate generalized theta divisors Θr in the moduli spaces UC(r,r) of semistable vector bundles on a curve C of genus 2. We provide a desingularization Φ of Θr in terms of a projective bundle π:P(V)→UC(r−1,r) which parametrizes extensions of stable vector bundles on the base by OC. Then, we study the composition of Φ with the well known theta map θ. We prove that, when it is restricted to the general fiber of π, we obtain a linear embedding.
Brivio, S., Favale, F. (2019). Genus 2 curves and generalized theta divisors. BULLETIN DES SCIENCES MATHEMATIQUES, 155, 112-140 [10.1016/j.bulsci.2019.05.002].
Genus 2 curves and generalized theta divisors
Brivio, S
;Favale, FF
2019
Abstract
In this paper we investigate generalized theta divisors Θr in the moduli spaces UC(r,r) of semistable vector bundles on a curve C of genus 2. We provide a desingularization Φ of Θr in terms of a projective bundle π:P(V)→UC(r−1,r) which parametrizes extensions of stable vector bundles on the base by OC. Then, we study the composition of Φ with the well known theta map θ. We prove that, when it is restricted to the general fiber of π, we obtain a linear embedding.
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