Reduced Čech complexes and computing higher direct images under toric maps
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866908325556256768 |
|---|---|
| author | Roth, Mike Zotine, Sasha |
| author_facet | Roth, Mike Zotine, Sasha |
| contents | This paper has three main goals :
(1) To give an axiomatic formulation of the construction of "reduced Čech complexes", complexes using fewer than the usual number of intersections but still computing cohomology of an appropriate class of sheaves;
(2) To give a construction of such a reduced Čech complex for every semi-proper toric variety $X$, where every open used in the complex is torus stable, and such that the cell complex governing the reduced Čech complex has dimension the cohomological dimension of $X$; and
(3) to give an algorithm to compute the higher direct images of line bundles relative to a toric fibration between smooth proper toric varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12903 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reduced Čech complexes and computing higher direct images under toric maps Roth, Mike Zotine, Sasha Algebraic Geometry 14M25, 14F06, 14Q99 This paper has three main goals : (1) To give an axiomatic formulation of the construction of "reduced Čech complexes", complexes using fewer than the usual number of intersections but still computing cohomology of an appropriate class of sheaves; (2) To give a construction of such a reduced Čech complex for every semi-proper toric variety $X$, where every open used in the complex is torus stable, and such that the cell complex governing the reduced Čech complex has dimension the cohomological dimension of $X$; and (3) to give an algorithm to compute the higher direct images of line bundles relative to a toric fibration between smooth proper toric varieties. |
| title | Reduced Čech complexes and computing higher direct images under toric maps |
| topic | Algebraic Geometry 14M25, 14F06, 14Q99 |
| url | https://arxiv.org/abs/2504.12903 |