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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.12647 |
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| _version_ | 1866911209983311872 |
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| author | Alecci, Gessica Graffeo, Michele Stokes, Alexander |
| author_facet | Alecci, Gessica Graffeo, Michele Stokes, Alexander |
| contents | The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry side, which is applied to differential and discrete Painlevé equations on the integrable systems side. Along the way we also discuss the theory of resolution of indeterminacies, which is applied to the cohomological computation of algebraic entropy of birational transformations of projective spaces, which is closely related to the integrability of the discrete systems they define. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_12647 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classical Algebraic Geometry and Discrete Integrable Systems Alecci, Gessica Graffeo, Michele Stokes, Alexander Algebraic Geometry Mathematical Physics 14E05, 14J26, 34M55, 39A45 The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry side, which is applied to differential and discrete Painlevé equations on the integrable systems side. Along the way we also discuss the theory of resolution of indeterminacies, which is applied to the cohomological computation of algebraic entropy of birational transformations of projective spaces, which is closely related to the integrability of the discrete systems they define. |
| title | Classical Algebraic Geometry and Discrete Integrable Systems |
| topic | Algebraic Geometry Mathematical Physics 14E05, 14J26, 34M55, 39A45 |
| url | https://arxiv.org/abs/2510.12647 |