English

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