English

Birational Classification of Orbifold Compactified Jacobians

Algebraic Geometry 2026-05-06 v1

Abstract

We study the equivariant orbifold birational classification problem for families of toroidal compactifications of a group GG over a toroidal base, in the cases where GG is an algebraic torus or a semiabelian scheme. The classification is reduced to the problem of finding the minimal orbifold toroidal compactifications of GG 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.

Keywords

Cite

@article{arxiv.2605.03835,
  title  = {Birational Classification of Orbifold Compactified Jacobians},
  author = {Jeremy Feusi and Sam Molcho},
  journal= {arXiv preprint arXiv:2605.03835},
  year   = {2026}
}

Comments

50 pages, comments are welcome!

R2 v1 2026-07-01T12:50:58.927Z