Cosection Localization for D-Manifolds and (−2)-Shifted Symplectic Derived Schemes, Revisited

Michail Savvas

doi:10.48550/arxiv.2309.03066

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Cosection Localization for D-Manifolds and (−2)-Shifted Symplectic Derived Schemes, Revisited

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Cosection Localization for D-Manifolds and (−2)-Shifted Symplectic Derived Schemes, Revisited

Michail Savvas

arXiv (Cornell University)

09/06/2023

DOI: 10.48550/arxiv.2309.03066

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Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

This is a continuation of prior work of the author on cosection localization for d-manifolds. We construct reduced virtual fundamental classes for derived manifolds with surjective cosections and cosection localized virtual fundamental classes for (−2)-shifted symplectic derived schemes in larger generality. Moreover, using recent results of Oh-Thomas, we show that the algebraic and differential geometric constructions of reduced and cosection localized virtual fundamental classes of (−2)-shifted symplectic derived schemes yield the same result in homology. We obtain applications towards the construction and integrality of reduced invariants in Donaldson-Thomas theory of Calabi-Yau fourfolds.

Mathematics - Algebraic Geometry

Mathematics - Differential Geometry

Details

Title: Subtitle: Cosection Localization for D-Manifolds and (−2)-Shifted Symplectic Derived Schemes, Revisited
Creators: Michail Savvas
Resource Type: Preprint
Publication Details: arXiv (Cornell University)
DOI: 10.48550/arxiv.2309.03066
eISSN: 2331-8422
Number of pages: 24 pages
Language: English
Date posted: 09/06/2023
Academic Unit: Mathematics
Record Identifier: 9984696868402771

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