Date: Friday, 31st May 2024
Time: 4pm to 5pm
Venue: Ramanujan Hall
Speaker: Debaditya Raychaudhury, University of Arizona
Title: Ulrich subvarieties and non-existence of low rank Ulrich bundles on complete intersections
Abstract: We characterize the existence of an Ulrich vector bundle on a variety $X\subset{\bf P}^N$ in terms of the existence of a subvariety satisfying certain conditions. Then we use this fact to prove that $(X,\mathcal{O}_X(a))$ where $X$ is a complete intersection of dimension $n\geq 4$, which if n = 4, is either ${\bf P}^4$ with $a\geq 2$, or very general with $a\geq 1$ and not of type (2), (2, 2), does not carry any Ulrich bundles of rank $r\leq 3$. Work in collaboration with A.F. Lopez.