Fano varieties with large pseudoindex and non-free rational curves

Autor:	Watanabe, Kiwamu
Rok vydání:	2023
Předmět:	Mathematics - Algebraic Geometry Mathematics - Complex Variables Mathematics - Differential Geometry 14J40 14J45 14E30
Druh dokumentu:	Working Paper
Popis:	For $n\geq 4$, let $X$ be a complex smooth Fano $n$-fold whose minimal anticanonical degree of non-free rational curves on $X$ is at least $n-2$. We classify extremal contractions of such varieties. As an application, we obtain a classification of Fano fourfolds with pseudoindex and Picard number greater than one. Combining this result with previous results, we complete the classification of smooth Fano $n$-folds with pseudoindex at least $n-2$ and Picard number greater than one. This can be seen as a generalization of various previous results. We also discuss the relations between pseudoindex and other invariants of Fano varieties. Comment: 27 pages. I have combined previous versions of this paper and paper arXiv:2402.14283 into this one paper. The content has been significantly revised, including the title and introduction
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2309.03438 Zobrazit plný text záznamu View this record from Arxiv