Fano schemes of complete intersections in toric varieties
| Autor: | Tyler L. Kelly, Nathan Ilten |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Intersection theory
medicine.medical_specialty General Mathematics 010102 general mathematics Dimension (graph theory) Zero (complex analysis) Toric variety Fano plane 01 natural sciences Linear subspace Upper and lower bounds Combinatorics Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry 0103 physical sciences FOS: Mathematics medicine 010307 mathematical physics 0101 mathematics Algebraic Geometry (math.AG) 14M25 14M10 14C05 14N15 Mathematics |
| Zdroj: | Mathematische Zeitschrift. 300:1529-1556 |
| ISSN: | 1432-1823 0025-5874 |
| DOI: | 10.1007/s00209-021-02809-4 |
| Popis: | We study Fano schemes $F_k(X)$ for complete intersections $X$ in a projective toric variety $Y\subset \mathbb{P}^n$. Our strategy is to decompose $F_k(X)$ into closed subschemes based on the irreducible decomposition of $F_k(Y)$ as studied by Ilten and Zotine. We define the expected dimension for these subschemes, which always gives a lower bound on the actual dimension. Under additional assumptions, we show that these subschemes are non-empty and smooth of the expected dimension. Using tools from intersection theory, we can apply these results to count the number of linear subspaces in $X$ when the expected dimension of $F_k(X)$ is zero. Comment: 28 pages, minor revision, to appear in Math Z |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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