Exponential map in DT theory
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915628537872384 |
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| author | Kaubrys, Sarunas |
| author_facet | Kaubrys, Sarunas |
| contents | This paper studies the Cohomological Donaldson-Thomas theory of loop stacks of $0$-shifted symplectic stacks. In particular, we compare $(-1)$-shifted tangent stacks of these moduli problems, which we view as additive, to loop stacks, which we view as multiplicative, via an exponential map that preserves induced $(-1)$-shifted symplectic structures. As an application, we prove for certain moduli of objects of $2$-Calabi-Yau categories a loop dimensional reduction theorem for the loop stacks of these moduli spaces. Finally, we prove a loop version of nonabelian Hodge theory for stacks in the $\mathrm{GL}_n$ case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_16261 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exponential map in DT theory Kaubrys, Sarunas Algebraic Geometry Representation Theory This paper studies the Cohomological Donaldson-Thomas theory of loop stacks of $0$-shifted symplectic stacks. In particular, we compare $(-1)$-shifted tangent stacks of these moduli problems, which we view as additive, to loop stacks, which we view as multiplicative, via an exponential map that preserves induced $(-1)$-shifted symplectic structures. As an application, we prove for certain moduli of objects of $2$-Calabi-Yau categories a loop dimensional reduction theorem for the loop stacks of these moduli spaces. Finally, we prove a loop version of nonabelian Hodge theory for stacks in the $\mathrm{GL}_n$ case. |
| title | Exponential map in DT theory |
| topic | Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2511.16261 |