Toric differential forms and periods of complete intersections
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929324219695104 |
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| author | Loyola, Roberto Villaflor |
| author_facet | Loyola, Roberto Villaflor |
| contents | Let $n$ be an even natural number. We compute the periods of any $\frac{n}{2}$-dimensional complete intersection algebraic cycle inside an $n$-dimensional non-degenerated intersection of a projective simplicial toric variety. Using this information we determine the cycle class of such algebraic cycles. As part of the proof we develop a toric generalization of a classical theorem of Macaulay about complete intersection Artin Gorenstein rings, and we generalize an algebraic cup formula for residue forms due to Carlson and Griffiths to the toric setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_12931 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Toric differential forms and periods of complete intersections Loyola, Roberto Villaflor Algebraic Geometry 14C25, 14C30, 14M25, 13H10 Let $n$ be an even natural number. We compute the periods of any $\frac{n}{2}$-dimensional complete intersection algebraic cycle inside an $n$-dimensional non-degenerated intersection of a projective simplicial toric variety. Using this information we determine the cycle class of such algebraic cycles. As part of the proof we develop a toric generalization of a classical theorem of Macaulay about complete intersection Artin Gorenstein rings, and we generalize an algebraic cup formula for residue forms due to Carlson and Griffiths to the toric setting. |
| title | Toric differential forms and periods of complete intersections |
| topic | Algebraic Geometry 14C25, 14C30, 14M25, 13H10 |
| url | https://arxiv.org/abs/2306.12931 |