Torelli theorem for the moduli spaces of twisted vector bundles on smooth projective curves
Abstract
We prove Torelli theorems for moduli space of twisted vector bundles on smooth projective curves over an arbitrary field of characteristic ≠ 2. A twisted Hitchin construction recovers the curve in higher rank and degree, with partial recovery of the twisting class. For rank two with trivial determinant, we recover the curve and the Brauer class from the moduli stack through an ordered Kummer cover and its polarized Jacobian torsor. For odd determinant on hyperelliptic curves, residual gerbes give a relative Desale--Ramanan construction without an actual determinant line bundle over the ground field. An intrinsic polarized Fano torsor recovers the curve and the class, and a corrected polarization obstruction recovers the determinant gerbe. We also give a twisted Newstead construction in genus two, with an explicit descent condition for its converse, and period--index applications. This is the second part in a series of two papers.
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BibTeX
@misc{ghosh2026torelli,
title = {{Torelli theorem for the moduli spaces of twisted vector bundles on smooth projective curves}},
author = {Soham Ghosh and Ting Gong and Max Lieblich},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25500},
eprint = {2610.25500},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25500},
}
RIS
TY - UNPB
TI - Torelli theorem for the moduli spaces of twisted vector bundles on smooth projective curves
AU - Soham Ghosh
AU - Ting Gong
AU - Max Lieblich
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.25500
UR - https://arxiv.org/abs/2610.25500
AB - We prove Torelli theorems for moduli space of twisted vector bundles on smooth projective curves over an arbitrary field of characteristic ≠ 2. A twisted Hitchin construction recovers the curve in higher rank and degree, with partial recovery of the twisting class. For rank two with trivial determinant, we recover the curve and the Brauer class from the moduli stack through an ordered Kummer cover and its polarized Jacobian torsor. For odd determinant on hyperelliptic curves, residual gerbes give a relative Desale--Ramanan construction without an actual determinant line bundle over the ground field. An intrinsic polarized Fano torsor recovers the curve and the class, and a corrected polarization obstruction recovers the determinant gerbe. We also give a twisted Newstead construction in genus two, with an explicit descent condition for its converse, and period--index applications. This is the second part in a series of two papers.
ER -