Resurgence and perverse sheaves
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915696766615552 |
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| author | Kapranov, Mikhail Soibelman, Yan |
| author_facet | Kapranov, Mikhail Soibelman, Yan |
| contents | We propose a point of view on resurgence theory based on the study of perverse sheaves on the complex line carrying an algebraic structure with respect to additive convolution. In particular, we lift the concept of alien derivatives introduced originally by J. Écalle, to the framework of perverse sheaves and study its behavior under sheaf-theoretic convolution. The full fledged resurgence theory needs a (yet undeveloped) generalization of the concept of perverse sheaves allowing infinite, possibly dense, sets of singularities. We discuss possible approaches to defining such objects and some potential examples of them coming from Cohomological Hall Algebras, wall-crossing structures and Chern-Simons theory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_22718 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Resurgence and perverse sheaves Kapranov, Mikhail Soibelman, Yan Algebraic Geometry High Energy Physics - Theory Complex Variables Quantum Algebra Symplectic Geometry 14F43, 55N33 (Primary), 81T99 (Secondary) We propose a point of view on resurgence theory based on the study of perverse sheaves on the complex line carrying an algebraic structure with respect to additive convolution. In particular, we lift the concept of alien derivatives introduced originally by J. Écalle, to the framework of perverse sheaves and study its behavior under sheaf-theoretic convolution. The full fledged resurgence theory needs a (yet undeveloped) generalization of the concept of perverse sheaves allowing infinite, possibly dense, sets of singularities. We discuss possible approaches to defining such objects and some potential examples of them coming from Cohomological Hall Algebras, wall-crossing structures and Chern-Simons theory. |
| title | Resurgence and perverse sheaves |
| topic | Algebraic Geometry High Energy Physics - Theory Complex Variables Quantum Algebra Symplectic Geometry 14F43, 55N33 (Primary), 81T99 (Secondary) |
| url | https://arxiv.org/abs/2512.22718 |