Geometry Seminar

 

University of Tor Vergata, Department of Mathematics

6^th of February 2024, 14:30-16:00, room “D’Antoni”

 

 

 

 

 

 

 

Some examples of Ulrich sheaves

 

Roberto Vacca

Tor Vergata

 

 

 

 

In this talk we will introduce Ulrich sheaves on projective algebraic varieties.
The corresponding notion for modules over rings originated from the work of Ulrich, but only after a paper by Eisenbud and Schreyer its geometric side received many attention due to the connection with determinantal and Pfaffian representations of (Chow forms of) varieties.
The main questions are existence of such sheaves and, if so, their minimal rank.
Positive answer to the first question is known for curves, surfaces (up to change of polarization), Veronese varieties, Segre varieties and complete intersections.
Outside those examples, very few is known in dimension at least 3; therefore we will focus on Fano 3-folds.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This talk is part of the activity of the MIUR Excellence Department Projects MathMod@TOV, and the PRIN 2022 Moduli Spaces and Birational Geometry