## Global shifted potentials for moduli spaces of sheaves on CY4

Publikation: Working paper/Preprint Working paperForskning

### Standard

Global shifted potentials for moduli spaces of sheaves on CY4. / Borisov, Dennis; Sheshmani, Artan; Yau, Shing-Tung.

ArXiv, 2019.

Publikation: Working paper/Preprint Working paperForskning

### Bibtex

@techreport{d0801e97c2fb46c5a960cffff564bd0b,
title = "Global shifted potentials for moduli spaces of sheaves on CY4",
abstract = " It is shown that any derived scheme over $\mathbb C$ equipped with a $-2$-shifted symplectic structure, and having a Hausdorff space of classical points, admits a globally defined Lagrangian distribution as a dg $\mathbb{C}^{\infty}$-manifold. The main tool for proving this theorem is a strictification result for Lagrangian distribution. It is shown that existence of a global Lagrangian distribution allows us to realize the moduli space of sheaves on Calabi-Yau fourfolds as a derived critical locus of a potential of degree $-1$ on the moduli space of $Spin(7)$ instantons. ",
keywords = "math.AG, hep-th, math.DG",
author = "Dennis Borisov and Artan Sheshmani and Shing-Tung Yau",
note = "33 pages, we appreciate any comments",
year = "2019",
month = aug,
day = "1",
language = "English",
publisher = "ArXiv",
type = "WorkingPaper",
institution = "ArXiv",

}

### RIS

TY - UNPB

T1 - Global shifted potentials for moduli spaces of sheaves on CY4

AU - Borisov, Dennis

AU - Sheshmani, Artan

AU - Yau, Shing-Tung

N1 - 33 pages, we appreciate any comments

PY - 2019/8/1

Y1 - 2019/8/1

N2 - It is shown that any derived scheme over $\mathbb C$ equipped with a $-2$-shifted symplectic structure, and having a Hausdorff space of classical points, admits a globally defined Lagrangian distribution as a dg $\mathbb{C}^{\infty}$-manifold. The main tool for proving this theorem is a strictification result for Lagrangian distribution. It is shown that existence of a global Lagrangian distribution allows us to realize the moduli space of sheaves on Calabi-Yau fourfolds as a derived critical locus of a potential of degree $-1$ on the moduli space of $Spin(7)$ instantons.

AB - It is shown that any derived scheme over $\mathbb C$ equipped with a $-2$-shifted symplectic structure, and having a Hausdorff space of classical points, admits a globally defined Lagrangian distribution as a dg $\mathbb{C}^{\infty}$-manifold. The main tool for proving this theorem is a strictification result for Lagrangian distribution. It is shown that existence of a global Lagrangian distribution allows us to realize the moduli space of sheaves on Calabi-Yau fourfolds as a derived critical locus of a potential of degree $-1$ on the moduli space of $Spin(7)$ instantons.

KW - math.AG

KW - hep-th

KW - math.DG

M3 - Working paper

BT - Global shifted potentials for moduli spaces of sheaves on CY4

PB - ArXiv

ER -