On the Morita invariance of Categorical Enumerative Invariants

TL;DR

This paper extends the definition of Categorical Enumerative Invariants to Calabi-Yau A-infinity categories, proves their Morita invariance, and applies these results to derive new invariants for Calabi-Yau 3-folds.

Contribution

It introduces a Morita invariance proof for CEI and develops tools for unital, cyclic models of Calabi-Yau categories, including a unital Darboux theorem.

Findings

Proved Morita invariance of CEI.

Constructed unital and cyclic models for Calabi-Yau categories.

Computed CEI for new examples and derived invariants for Calabi-Yau 3-folds.

Abstract

Categorical Enumerative Invariants (CEI) are invariants associated with a unital, cyclic, smooth $A_\infty$-category and a splitting of its non-commutative Hodge filtration. In this paper, we extend the definition of CEI to Calabi-Yau $A_\infty$-categories with a splitting. Moreover, we formulate and prove the Morita invariance of CEI. As part of our proof, we develop tools to construct unital and cyclic models for Calabi-Yau categories. In particular, we prove a unital version of Kontsevich-Soibelman's Darboux theorem. As an application, we compute CEI in some new examples. Also, when applied to derived categories of coherent sheaves, our results yield new invariants of smooth, proper Calabi-Yau 3-folds.