Complex slices on a real variety
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909922530164736 |
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| author | Viro, Oleg |
| author_facet | Viro, Oleg |
| contents | Let $X$ be a real algebraic variety with set of complex points $X_{\mathbb C}$ and set of real points $X_{\mathbb R}$. A complex slice of $X$ is a transverse intersection of $X_{\mathbb R}$ with a complex subvariety $V$ of $X_{\mathbb C}$. Complex slices are real algebraic varieties of a very special kind. They are cooriented, realize an integer cohomology class. A codimension 2 projective variety is a slice, iff it is a base of pencil of real algebraic hypersurfaces. We prove an upper bound for the linking number of a real projective curve bounding in its complexification with a slice of codimension two. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19929 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Complex slices on a real variety Viro, Oleg Algebraic Geometry Geometric Topology 14P25, 14F45, 57R19, 55M25, 55N25 Let $X$ be a real algebraic variety with set of complex points $X_{\mathbb C}$ and set of real points $X_{\mathbb R}$. A complex slice of $X$ is a transverse intersection of $X_{\mathbb R}$ with a complex subvariety $V$ of $X_{\mathbb C}$. Complex slices are real algebraic varieties of a very special kind. They are cooriented, realize an integer cohomology class. A codimension 2 projective variety is a slice, iff it is a base of pencil of real algebraic hypersurfaces. We prove an upper bound for the linking number of a real projective curve bounding in its complexification with a slice of codimension two. |
| title | Complex slices on a real variety |
| topic | Algebraic Geometry Geometric Topology 14P25, 14F45, 57R19, 55M25, 55N25 |
| url | https://arxiv.org/abs/2511.19929 |