Back to Algebraic Geometry Seminar: Spring 2023
Algebraic Geometry Seminar
Date: Tuesday, Apr 25, 2023
Time: 3:30PM - 4:30PM
Location: LCB 323
@ 3pm
Kelly Jabbusch
University of Michigan - Dearborn
Title |
The minimal projective bundle dimension and toric 2-Fano manifolds Note the unusual time! |
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) ≥ 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 Geometry