Geometric families of degenerations from mutations of polytopes
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916544162824192 |
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| author | Escobar, Laura Harada, Megumi Manon, Christopher |
| author_facet | Escobar, Laura Harada, Megumi Manon, Christopher |
| contents | We introduce the notion of a polyptych lattice, which encodes a collection of lattices related by piecewise linear bijections. We initiate a study of the new theory of convex geometry and polytopes associated to polyptych lattices. In certain situations, such a polytope associated to a polyptych lattice encodes a compactification of an affine variety whose coordinate ring can be equipped with a valuation into a certain semialgebra associated to the polyptych lattice. We show that aspects of the geometry of the compactification can be understood combinatorially; for instance, under some hypotheses, the resulting compactifications are arithmetically Cohen-Macaulay, and have finitely generated class group and finitely generated Cox rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01785 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometric families of degenerations from mutations of polytopes Escobar, Laura Harada, Megumi Manon, Christopher Algebraic Geometry Primary: 14M15, 52B20, Secondary: 13F60, 14T15, 14T20 We introduce the notion of a polyptych lattice, which encodes a collection of lattices related by piecewise linear bijections. We initiate a study of the new theory of convex geometry and polytopes associated to polyptych lattices. In certain situations, such a polytope associated to a polyptych lattice encodes a compactification of an affine variety whose coordinate ring can be equipped with a valuation into a certain semialgebra associated to the polyptych lattice. We show that aspects of the geometry of the compactification can be understood combinatorially; for instance, under some hypotheses, the resulting compactifications are arithmetically Cohen-Macaulay, and have finitely generated class group and finitely generated Cox rings. |
| title | Geometric families of degenerations from mutations of polytopes |
| topic | Algebraic Geometry Primary: 14M15, 52B20, Secondary: 13F60, 14T15, 14T20 |
| url | https://arxiv.org/abs/2408.01785 |