Lefschetz duality for local cohomology
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2022
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917870511849472 |
|---|---|
| author | Varbaro, Matteo Yu, Hongmiao |
| author_facet | Varbaro, Matteo Yu, Hongmiao |
| contents | Since the 1974 paper by Peskine and Szpiro, liaison theory via complete intersections, and more generally via Gorenstein varieties, has become a standard tool kit in commutative algebra and algebraic geometry, allowing to compare algebraic features of linked varieties. In this paper we develop a liaison theory via quasi-Gorenstein varieties, a much broader class than Gorenstein varieties: it is not misleading to think that quasi-Gorenstein rings are to Gorenstein rings as manifolds are to spheres. As applications, we derive a connectedness property of quasi-Gorenstein subspace arrangements generalizing previous results by Benedetti and the second author, and we deduce the classical topological Lefschetz duality via the Stanley-Reisner correspondence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_11504 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Lefschetz duality for local cohomology Varbaro, Matteo Yu, Hongmiao Commutative Algebra Algebraic Geometry Algebraic Topology Combinatorics 13C40, 14M10, 13D45, 05E40, 05E45, 13D09 Since the 1974 paper by Peskine and Szpiro, liaison theory via complete intersections, and more generally via Gorenstein varieties, has become a standard tool kit in commutative algebra and algebraic geometry, allowing to compare algebraic features of linked varieties. In this paper we develop a liaison theory via quasi-Gorenstein varieties, a much broader class than Gorenstein varieties: it is not misleading to think that quasi-Gorenstein rings are to Gorenstein rings as manifolds are to spheres. As applications, we derive a connectedness property of quasi-Gorenstein subspace arrangements generalizing previous results by Benedetti and the second author, and we deduce the classical topological Lefschetz duality via the Stanley-Reisner correspondence. |
| title | Lefschetz duality for local cohomology |
| topic | Commutative Algebra Algebraic Geometry Algebraic Topology Combinatorics 13C40, 14M10, 13D45, 05E40, 05E45, 13D09 |
| url | https://arxiv.org/abs/2208.11504 |