Fundamental Factorization of a GLSM. Part I, Construction / Ionut Ciocan-Fontanine [and four others].

Format:

Book

Author/Creator:

Ciocan-Fontanine, Ionut, author.

Series:

Memoirs of the American Mathematical Society ; Volume 289.

Memoirs of the American Mathematical Society Series ; Volume 289

Language:

English

Subjects (All):

Geometry, Algebraic.

Physical Description:

1 online resource (108 pages)

Edition:

First edition.

Place of Publication:

Providence, RI : American Mathematical Society, [2023]

Summary:

We define enumerative invariants associated to a hybrid Gauged Linear Sigma Model. We prove that in the relevant special cases these invariants recover both the Gromov-Witten type invariants defined by Chang-Li and Fan-Jarvis-Ruan using cosection localization as well as the FJRW type invariants constructed by Polishchuk-Vaintrob. The invariants are defined by constructing a "fundamental factorization" supported on the moduli space of Landau-Ginzburg maps to a convex hybrid model. This gives the kernel of a Fourier-Mukai transform; the associated map on Hochschild homology defines our theory.

Contents:

Cover

Title page

Chapter 1. Introduction

1.1. Background

1.2. Construction

1.3. Comparisons

1.4. Future work

1.5. Structure of the paper

1.6. Conventions and notations

Chapter 2. Overview of the construction

2.1. Input data

2.2. Landau-Ginzburg quasimaps

2.3. Stability conditions and moduli of stable LG maps

2.4. Hybrid models

2.5. The plan

Chapter 3. Factorizations

3.1. Derived categories of Landau-Ginzburg models

3.2. Derived functors

3.3. Koszul factorizations

3.4. Hochschild Homology

3.5. Comparisons

Chapter 4. Admissible resolutions of GLSMs

4.1. Setup

4.2. Admissible resolutions

4.3. Definition of the Polishchuk-Vaintrob factorization

4.4. On Condition 1

4.5. On Conditions 2 and 3

4.6. Support of the PV factorization

4.7. -charge equivariance

Chapter 5. Construction of a projective embedding

5.1. Convexity

5.2. Quasi-projective embeddings

5.3. Properties of moduli of LG maps

Chapter 6. The GLSM theory for convex hybrid models

6.1. The Fundamental Factorization

6.2. Independence of choices

6.3. Rigidified evaluation and the state space

6.4. The restricted state space

6.5. GLSM invariants

Chapter 7. Comparisons with other constructions

7.1. Comparison with Gromov-Witten theory and cosection localization

7.2. Comparison with the Polishchuk-Vaintrob construction

7.3. Comparison with other affine phases

Bibliography

Back Cover.

Notes:

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-7590-1