A hyperbolicity conjecture for adjoint bundles
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913815483908096 |
|---|---|
| author | Moraga, Joaquín Yeong, Wern |
| author_facet | Moraga, Joaquín Yeong, Wern |
| contents | Let $X$ be a $n$-dimensional smooth projective variety and $L$ be an ample Cartier divisor on $X$. We conjecture that a very general element of the linear system $|K_X+(3n+1)L|$ is a hyperbolic algebraic variety. This conjecture holds for some classical varieties: surfaces, products of projective spaces, and Grassmannians. In this article, we investigate the conjecture for $X$ a toric variety. We confirm the conjecture in the case of smooth projective toric varieties. When $X$ is a Gorenstein toric variety, we show that $|K_X+(3n+1)L|$ is pseudo hyperbolic. For a Gorenstein toric threefold $X$, we show that $|K_X+9L|$ is hyperbolic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_01811 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A hyperbolicity conjecture for adjoint bundles Moraga, Joaquín Yeong, Wern Algebraic Geometry 14J70 (Primary) 14M25, 14F17 (Secondary) Let $X$ be a $n$-dimensional smooth projective variety and $L$ be an ample Cartier divisor on $X$. We conjecture that a very general element of the linear system $|K_X+(3n+1)L|$ is a hyperbolic algebraic variety. This conjecture holds for some classical varieties: surfaces, products of projective spaces, and Grassmannians. In this article, we investigate the conjecture for $X$ a toric variety. We confirm the conjecture in the case of smooth projective toric varieties. When $X$ is a Gorenstein toric variety, we show that $|K_X+(3n+1)L|$ is pseudo hyperbolic. For a Gorenstein toric threefold $X$, we show that $|K_X+9L|$ is hyperbolic. |
| title | A hyperbolicity conjecture for adjoint bundles |
| topic | Algebraic Geometry 14J70 (Primary) 14M25, 14F17 (Secondary) |
| url | https://arxiv.org/abs/2412.01811 |