Birational Classification of Orbifold Compactified Jacobians
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913091166404608 |
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| author | Feusi, Jeremy Molcho, Sam |
| author_facet | Feusi, Jeremy Molcho, Sam |
| contents | We study the equivariant orbifold birational classification problem for families of toroidal compactifications of a group $G$ over a toroidal base, in the cases where $G$ is an algebraic torus or a semiabelian scheme. The classification is reduced to the problem of finding the minimal orbifold toroidal compactifications of $G$ in the world of logarithmic geometry, which is shown to be a combinatorial problem. We solve the problem for families of algebraic tori, Jacobians of families of nodal curves, and semiabelian schemes with abelian generic fiber. The general semiabelian case is reduced to an open conjecture. These results generalize and geometrically interpret recent results of Schmitt. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03835 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Birational Classification of Orbifold Compactified Jacobians Feusi, Jeremy Molcho, Sam Algebraic Geometry 14E99 14A21 We study the equivariant orbifold birational classification problem for families of toroidal compactifications of a group $G$ over a toroidal base, in the cases where $G$ is an algebraic torus or a semiabelian scheme. The classification is reduced to the problem of finding the minimal orbifold toroidal compactifications of $G$ in the world of logarithmic geometry, which is shown to be a combinatorial problem. We solve the problem for families of algebraic tori, Jacobians of families of nodal curves, and semiabelian schemes with abelian generic fiber. The general semiabelian case is reduced to an open conjecture. These results generalize and geometrically interpret recent results of Schmitt. |
| title | Birational Classification of Orbifold Compactified Jacobians |
| topic | Algebraic Geometry 14E99 14A21 |
| url | https://arxiv.org/abs/2605.03835 |