Lefschetz properties through a topological lens
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912153486753792 |
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| author | Seceleanu, Alexandra |
| author_facet | Seceleanu, Alexandra |
| contents | These lecture notes were prepared for the Lefschetz Preparatory School, a graduate summer course held in Krakow, May 6-10, 2024. They present the story of the algebraic Lefschetz properties from their origin in algebraic geometry to some recent developments in commutative algebra. The common thread of the notes is a bias towards topics surrounding the algebraic Lefschetz properties that have a topological flavor. These range from the Hard Lefschetz Theorem for cohomology rings to commutative algebraic analogues of these rings, namely artinian Gorenstein rings, and topologically motivated operations among such rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_08917 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lefschetz properties through a topological lens Seceleanu, Alexandra Commutative Algebra These lecture notes were prepared for the Lefschetz Preparatory School, a graduate summer course held in Krakow, May 6-10, 2024. They present the story of the algebraic Lefschetz properties from their origin in algebraic geometry to some recent developments in commutative algebra. The common thread of the notes is a bias towards topics surrounding the algebraic Lefschetz properties that have a topological flavor. These range from the Hard Lefschetz Theorem for cohomology rings to commutative algebraic analogues of these rings, namely artinian Gorenstein rings, and topologically motivated operations among such rings. |
| title | Lefschetz properties through a topological lens |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2412.08917 |