Hodge microsheaves on cotangent bundles and plumbings
Algebraic Geometry
2025-05-09 v2 Representation Theory
Symplectic Geometry
Abstract
We introduce and study the category of Hodge microsheaves which is a Hodge-version of the category of microsheaves for a certain class of holomorphic exact symplectic manifolds. We then study Hodge-theoretic version of wrapped sheaves and discuss applications in topology and representation theory. Namely, we study (1) Hain's Hodge structures on the cohomology of based loop spaces of algebraic varieties, and (2) the Koszul duality of Ginzburg algebras by Etg\"u-Lekili from a mixed geometric perspective.
Keywords
Cite
@article{arxiv.2502.04148,
title = {Hodge microsheaves on cotangent bundles and plumbings},
author = {Tatsuki Kuwagaki and Takahiro Saito},
journal= {arXiv preprint arXiv:2502.04148},
year = {2025}
}
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112 pages