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Involutions on moduli spaces of vector bundles and GIT quotients. (arXiv:1802.00654v1 [math.AG])
来源于:arXiv
Let $C$ be a hyperelliptic curve of genus $g \geq 3$. We give a new
description of the theta map for moduli spaces of rank 2 semistable vector
bundles with trivial determinant. In orther to do this, we describe a fibration
of (a birational model of) the moduli space, whose fibers are GIT quotients
$(\mathbb{P}^1)^{2g}//\operatorname{PGL(2)}$. Then, we use recent results of
Kumar to identify the restriction of the theta map to these GIT quotients with
some explicit osculating projection. As a corollary of this construction, we
obtain a birational equivalence between the ramification locus of the theta map
and a fibration in Kummer $(g-1)$-varieties over $\mathbb{P}^g$. 查看全文>>