Mathematics > Algebraic Geometry
[Submitted on 16 Nov 2016]
Title:Geometry of the moduli of parabolic bundles on elliptic curves
View PDFAbstract:The goal of this paper is the study of simple rank 2 parabolic vector bundles over a $2$-punctured elliptic curve $C$. We show that the moduli space of these bundles is a non-separated gluing of two charts isomorphic to $\mathbb{P}^1 \times \mathbb{P}^1$. We also showcase a special curve $\Gamma$ isomorphic to $C$ embedded in this space, and this way we prove a Torelli theorem.
This moduli space is related to the moduli space of semistable parabolic bundles over $\mathbb{P}^1$ via a modular map which turns out to be the 2:1 cover ramified in $\Gamma$. We recover the geometry of del Pezzo surfaces of degree 4 and we reconstruct all their automorphisms via elementary transformations of parabolic vector bundles.
Submission history
From: Néstor Fernández Vargas [view email][v1] Wed, 16 Nov 2016 19:44:35 UTC (157 KB)
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