Work

Torelli theorem for moduli stacks of vector bundles and principal G-bundles

Year: 2024

Type: article

Abstract: Given any irreducible smooth complex projective curve X , of genus at least 2, consider the moduli stack of vector bundles on X of fixed rank and determinant. It is proved that the isomorphism class of the stack uniquely determines the isomorphism class of the curve X and the rank of the vector bundles. The case of trivial determinant, rank 2 and genus 2 is specially interesting: the curve can be recovered from the moduli stack, but not from the moduli space (since this moduli space is P 3 thus independently of the curve). We also prove a Torelli theorem for moduli stacks of principal G -bundles on a curve of genus at least 3, where G is any non-abelian reductive group.

Source: Journal of Geometry and Physics

DOI: 10.1016/j.geomphys.2024.105350

Authors: David Alfaya, Indranil Biswas, Tomás L. Gómez, Swarnava Mukhopadhyay