The minimal projective bundle dimension and toric 2-Fano manifolds

Abstract: In this talk we will discuss higher Fano manifolds, which are Fano manifolds with positive higher Chern characters. In particular we will focus on toric 2-Fano manifolds. Motivated by the problem of classifying toric 2-Fano manifolds, we will introduce a new invariant for smooth projective toric varieties, the minimal projective bundle dimension, $m(X)$. This invariant $m(X)$ 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'll present a classification of smooth projective toric varieties with $m(X) \ge \dim(X)-2$, and show that projective spaces are the only 2-Fano manifolds among smooth projective toric varieties with $m(X)$ equal to $1$, $\dim(X)-2$, $\dim(X)-1$, or $\dim(X)$. This is joint work with Carolina Araujo, Roya Beheshti, Ana-Maria Castravet, Svetlana Makarova, Enrica Mazzon, and Nivedita Viswanathan.

algebraic geometrycombinatorics

Audience: researchers in the topic

Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html