On the Morita invariance of Categorical Enumerative Invariants
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912382567055360 |
|---|---|
| author | Amorim, Lino Tu, Junwu |
| author_facet | Amorim, Lino Tu, Junwu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_02744 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the Morita invariance of Categorical Enumerative Invariants Amorim, Lino Tu, Junwu Algebraic Geometry K-Theory and Homology Symplectic Geometry 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. |
| title | On the Morita invariance of Categorical Enumerative Invariants |
| topic | Algebraic Geometry K-Theory and Homology Symplectic Geometry |
| url | https://arxiv.org/abs/2209.02744 |