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Moduli Spaces of Twisted Endomorphisms and Euler Characteristics
Abstract
For a (quasi)projective variety X and an automorphism f of X, we define moduli spaces of twisted endomorphisms of sheaves on X. If the automorphism f has finite order, we construct a sheaf of noncommutative algebras π0(f) and show that sheaves with a twisted endomorphism can be described as π0(f)-modules. We compute the topological Euler characteristics of Hilbert schemes of points of the algebra π0(f), generalizing the answer for the case where f is the identity automorphism.
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BibTeX
@misc{korde2026moduli,
title = {{Moduli Spaces of Twisted Endomorphisms and Euler Characteristics}},
author = {Atharva Korde},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30343},
eprint = {2609.30343},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30343},
}
RIS
TY - UNPB
TI - Moduli Spaces of Twisted Endomorphisms and Euler Characteristics
AU - Atharva Korde
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30343
UR - https://arxiv.org/abs/2609.30343
AB - For a (quasi)projective variety X and an automorphism f of X, we define moduli spaces of twisted endomorphisms of sheaves on X. If the automorphism f has finite order, we construct a sheaf of noncommutative algebras π_0(f) and show that sheaves with a twisted endomorphism can be described as π_0(f)-modules. We compute the topological Euler characteristics of Hilbert schemes of points of the algebra π_0(f), generalizing the answer for the case where f is the identity automorphism.
ER -