On a Grauert-Riemenschneider vanishing theorem in dimension 3
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915604047331328 |
|---|---|
| author | Ajit, Rahul |
| author_facet | Ajit, Rahul |
| contents | Suppose $R$ is an excellent ring of dimension $3$ and has rational singularities. Let $π:X \longrightarrow \mathrm{Spec} \ R$ be a blow-up and $ϕ: W \longrightarrow X$ be any projective, birational morphism such that $X$ and $W$ are both normal, Cohen-Macaulay, and have pseudorational singularities in codimension $2$. Then $R^{i}ϕ_{*}ω_{W}=0 \ \text{ and }R^{i}π_{*}ω_{X} = 0$ for all $i>0$ and $X$ has rational singularities. We use this result to prove Lipman's vanishing conjecture in dimension $3$ for arbitrary characteristics and provide a few applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04906 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a Grauert-Riemenschneider vanishing theorem in dimension 3 Ajit, Rahul Algebraic Geometry Commutative Algebra 14F17, 14B05, 13A30 Suppose $R$ is an excellent ring of dimension $3$ and has rational singularities. Let $π:X \longrightarrow \mathrm{Spec} \ R$ be a blow-up and $ϕ: W \longrightarrow X$ be any projective, birational morphism such that $X$ and $W$ are both normal, Cohen-Macaulay, and have pseudorational singularities in codimension $2$. Then $R^{i}ϕ_{*}ω_{W}=0 \ \text{ and }R^{i}π_{*}ω_{X} = 0$ for all $i>0$ and $X$ has rational singularities. We use this result to prove Lipman's vanishing conjecture in dimension $3$ for arbitrary characteristics and provide a few applications. |
| title | On a Grauert-Riemenschneider vanishing theorem in dimension 3 |
| topic | Algebraic Geometry Commutative Algebra 14F17, 14B05, 13A30 |
| url | https://arxiv.org/abs/2511.04906 |