Скачать или смотреть Kelly Jabbusch (Michigan)

Kelly Jabbusch (Michigan)
25 May 2023

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

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.

Slides for this talk are available at:
https://kasprzyk.work/seminars/pdf/Ja...

Visit the Online Algebraic Geometry Seminar webpage at:
https://kasprzyk.work/seminars/ag.html