On the Smith-Thom deficiency of Hilbert squares
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866916686801666048 |
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| author | Kharlamov, Viatcheslav Răsdeaconu, Rareş |
| author_facet | Kharlamov, Viatcheslav Răsdeaconu, Rareş |
| contents | We give an expression for the Smith-Thom deficiency of the Hilbert square $X^{[2]}$ of a smooth real algebraic variety $X$ in terms of the rank of a suitable Mayer-Vietoris mapping in several situations. As a consequence, we establish a necessary and sufficient condition for the maximality of $X^{[2]}$ in the case of projective complete intersections, and show that with a few exceptions no real nonsingular projective complete intersection of even dimension has maximal Hilbert square. We also provide new examples of smooth real algebraic varieties with maximal Hilbert square. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_19120 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Smith-Thom deficiency of Hilbert squares Kharlamov, Viatcheslav Răsdeaconu, Rareş Algebraic Geometry Algebraic Topology Geometric Topology 14P25, 14C05, 14J99 We give an expression for the Smith-Thom deficiency of the Hilbert square $X^{[2]}$ of a smooth real algebraic variety $X$ in terms of the rank of a suitable Mayer-Vietoris mapping in several situations. As a consequence, we establish a necessary and sufficient condition for the maximality of $X^{[2]}$ in the case of projective complete intersections, and show that with a few exceptions no real nonsingular projective complete intersection of even dimension has maximal Hilbert square. We also provide new examples of smooth real algebraic varieties with maximal Hilbert square. |
| title | On the Smith-Thom deficiency of Hilbert squares |
| topic | Algebraic Geometry Algebraic Topology Geometric Topology 14P25, 14C05, 14J99 |
| url | https://arxiv.org/abs/2310.19120 |