Extremal effective curves and non-semiample line bundles on $\overline{\rm{M}}_{g,n}$
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911305924870144 |
|---|---|
| author | Choi, Daebeom |
| author_facet | Choi, Daebeom |
| contents | We develop a new method for establishing the extremality in the closed cone of effective curves on the moduli space of curves and determine the extremality of many boundary $1$-strata. As a consequence, by using a general criterion for non-semiampleness which extends Keel's argument, we demonstrate that a substantial portion of the cone of nef divisors of $\overline{\mathrm{M}}_{g,n}$ is not semiample. As an application, we construct the first explicit example of a non-contractible extremal ray of the closed cone of effective curves on $\overline{\mathrm{M}}_{3,n}$. Our method relies on two main ingredients: (1) the construction of a new collection of nef divisors on $\overline{\mathrm{M}}_{g,n}$, and (2) the identification of a tractable inductive structure on the Picard group, arising from Knudsen's construction of $\overline{\mathrm{M}}_{g,n}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_02019 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extremal effective curves and non-semiample line bundles on $\overline{\rm{M}}_{g,n}$ Choi, Daebeom Algebraic Geometry 14H10, 14G17 We develop a new method for establishing the extremality in the closed cone of effective curves on the moduli space of curves and determine the extremality of many boundary $1$-strata. As a consequence, by using a general criterion for non-semiampleness which extends Keel's argument, we demonstrate that a substantial portion of the cone of nef divisors of $\overline{\mathrm{M}}_{g,n}$ is not semiample. As an application, we construct the first explicit example of a non-contractible extremal ray of the closed cone of effective curves on $\overline{\mathrm{M}}_{3,n}$. Our method relies on two main ingredients: (1) the construction of a new collection of nef divisors on $\overline{\mathrm{M}}_{g,n}$, and (2) the identification of a tractable inductive structure on the Picard group, arising from Knudsen's construction of $\overline{\mathrm{M}}_{g,n}$. |
| title | Extremal effective curves and non-semiample line bundles on $\overline{\rm{M}}_{g,n}$ |
| topic | Algebraic Geometry 14H10, 14G17 |
| url | https://arxiv.org/abs/2511.02019 |