|Date: Wednesday, December 05, 2018
Location: 4096 East Hall (4:00 PM to 5:20 PM)
Title: Fujita's conjecture and Seshadri constants
Abstract: Abstract: Let X be a smooth 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, we present a new approach to Fujita's conjecture using Seshadri constants and positive characteristic methods. Our technique recovers known cases of Fujita's conjecture over the complex numbers, without the use of vanishing theorems, and proves new results for complex varieties with rational singularities.
Speaker: Takumi Murayama
Institution: University of MIchigan
Event Organizer: Karen Smith