Automorphism group of the moduli space of parabolic vector bundles with fixed degree

D. Alfaya

Bulletin des Sciences Mathématiques Vol. 175, pp. 103112-1 - 103112-26

Summary:

We find all possible isomorphisms and 3-birational maps (i.e., birational maps which induce an isomorphism between open subsets whose respective complements have codimension at least 3) between moduli spaces of parabolic vector bundles with fixed degree. We prove that every 3-birational map can be described as a composition of tensorization by a fixed line bundle, Hecke transformations, dualization, taking pullback by an isomorphism between the curves and the action of the group of automorphisms of the Jacobian variety of the curve which fix the r-torsion. In particular, we prove a Torelli type theorem, stating that the 3-birational class of the moduli space determines the isomorphism class of the curve.

Keywords: Parabolic vector bundle; Moduli space; Automorphism group; Extended Torelli theorem; Birational geometry; Stability chambers

JCR Impact Factor and WoS quartile: 1,300 - Q3 (2022); 1,300 - Q2 (2023)

DOI reference: https://doi.org/10.1016/j.bulsci.2022.103112

Published on paper: March 2022.

Published on-line: January 2022.

Citation:
D. Alfaya, Automorphism group of the moduli space of parabolic vector bundles with fixed degree. Bulletin des Sciences Mathématiques. Vol. 175, pp. 103112-1 - 103112-26, March 2022. [Online: January 2022]