Positivity of the exterior power of the tangent bundles

Autor:	Watanabe, Kiwamu
Rok vydání:	2022
Předmět:	Mathematics - Algebraic Geometry Mathematics - Complex Variables Mathematics - Differential Geometry
Druh dokumentu:	Working Paper
Popis:	Let $X$ be a complex smooth projective variety such that the exterior power of the tangent bundle $\bigwedge^{r} T_X$ is nef for some $1\leq r<\dim X$. We prove that, up to an \'etale cover, $X$ is a Fano fiber space over an Abelian variety. This gives generalizations of the structure theorem of varieties with nef tangent bundle by Demailly, Peternell and Schneider and that of varieties with nef $\bigwedge^{2} T_X$ by the author. Our result also gives an answer to a question raised by Li, Ou and Yang for varieties with strictly nef $\bigwedge^{r} T_X$ when $r < \dim X$. Comment: 6 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2208.06735 Zobrazit plný text záznamu View this record from Arxiv