The minimal projective bundle dimension and toric $2$-Fano manifolds

Autor:	Araujo, Carolina, Beheshti, Roya, Castravet, Ana-Maria, Jabbusch, Kelly, Makarova, Svetlana, Mazzon, Enrica, Viswanathan, Nivedita, Reynolds, Will
Rok vydání:	2023
Předmět:	Mathematics - Algebraic Geometry 14J45 14M25 (Primary) 14H10 14E05 (Secondary)
Druh dokumentu:	Working Paper
Popis:	Motivated by the problem of classifying toric $2$-Fano manifolds, we introduce a new invariant for smooth projective toric varieties, the minimal projective bundle dimension. This invariant $m(X)\in\{1, \dots,\dim(X)\}$ captures the minimal degree of a dominating family of rational curves on $X$ or, equivalently, the minimal length of a centrally symmetric primitive relation for the fan of $X$. We classify smooth projective toric varieties with $m(X)\geq \dim(X)-2$, and show that projective spaces are the only $2$-Fano manifolds among smooth projective toric varieties with $m(X)\in\{1, \dim(X)-2,\dim(X)-1,\dim(X)\}$. Comment: 32 pages, 1 figure. Comments welcome. V2: expanded Remark 2.11, added a citation
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2301.00883 Zobrazit plný text záznamu View this record from Arxiv