EVENT DETAILS AND ABSTRACT

Title: Fujita-type conjectures and Seshadri constants
Speaker: Takumi Murayama
Speaker Info: University of Michigan
Brief Description:
Special Note:
Abstract:

Let X be a smooth complex projective variety of dimension n and let L be an ample divisor on X. In 1988, Fujita conjectured that K+(n+1)L is globally generated and K+(n+2)L is very ample, where K is the canonical divisor on X. To tackle this conjecture, Demailly introduced Seshadri constants, which measure the positivity of L at a point x in X. While examples of Miranda seemed to indicate that Seshadri constants could not be used to prove Fujita's conjecture, Seshadri constants still give information about global generation at general points. We present joint work with Yajnaseni Dutta, which exploits Seshadri constants to give positive evidence toward Popa and Schnell's relative version of Fujita's conjecture, and an extension to higher-order jets, which is joint with Mihai Fulger. We also describe how despite Miranda's examples, Seshadri constants can still be used to recover some known results toward Fujita's conjecture.