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arXiv · 1910.05593

Fano Schemes of Complete Intersections in Toric Varieties

Nathan Ilten·Tyler L. Kelly
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Abstract

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.

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Nathan Ilten, Tyler L. Kelly. 2019-10-12. Fano Schemes of Complete Intersections in Toric Varieties. https://arxiv.org/abs/1910.05593

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