The MMP singularities of GIT versus Baily-Borel compactifications for the ball quotient case
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866915521394376704 |
|---|---|
| author | Shen, Dali |
| author_facet | Shen, Dali |
| contents | When the geometric invariant theory and the Baily-Borel theory both apply to a moduli space, the two resulting compactifications do not necessarily coincide. They usually differ by a birational transformation in terms of an arrangement, for which the general pattern was firstly described by Looijenga. In this paper, we compare the MMP singularities on both sides for the ball quotient case. We show that if the relevant arrangement is nonempty, the birational transformation from the GIT compactification to the Baily-Borel compactification turns non-log canonical singularities to log canonical singularities. We illustrate this with the moduli spaces of quartic curves, rational elliptic surfaces and cubic threefolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_24412 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The MMP singularities of GIT versus Baily-Borel compactifications for the ball quotient case Shen, Dali Algebraic Geometry When the geometric invariant theory and the Baily-Borel theory both apply to a moduli space, the two resulting compactifications do not necessarily coincide. They usually differ by a birational transformation in terms of an arrangement, for which the general pattern was firstly described by Looijenga. In this paper, we compare the MMP singularities on both sides for the ball quotient case. We show that if the relevant arrangement is nonempty, the birational transformation from the GIT compactification to the Baily-Borel compactification turns non-log canonical singularities to log canonical singularities. We illustrate this with the moduli spaces of quartic curves, rational elliptic surfaces and cubic threefolds. |
| title | The MMP singularities of GIT versus Baily-Borel compactifications for the ball quotient case |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2509.24412 |