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Article Dans Une Revue Nagoya Mathematical Journal Année : 2022

THE HYPERELLIPTIC THETA MAP AND OSCULATING PROJECTIONS

Résumé

Let C be a hyperelliptic curve of genus $g \geq 3$ . In this paper, we give a new geometric description of the theta map for moduli spaces of rank 2 semistable vector bundles on C with trivial determinant. In order to do this, we describe a fibration of (a birational model of) the moduli space, whose fibers are GIT quotients $(\mathbb {P}^1)^{2g}//\text {PGL(2)}$ . Then, we identify the restriction of the theta map to these GIT quotients with some explicit degree 2 osculating projection. As a corollary of this construction, we obtain a birational inclusion of a fibration in Kummer $(g-1)$ -varieties over $\mathbb {P}^g$ inside the ramification locus of the theta map.

Dates et versions

hal-03413234 , version 1 (03-11-2021)

Identifiants

Citer

Michele Bolognesi, Néstor Fernández Vargas. THE HYPERELLIPTIC THETA MAP AND OSCULATING PROJECTIONS. Nagoya Mathematical Journal, 2022, 245, pp.206-228. ⟨10.1017/nmj.2020.37⟩. ⟨hal-03413234⟩
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