Nathan Chen (Columbia)
Tuesday, November 21, 2023 - 2:30pm
PDL C-38
Main talk (2:30pm)
Title: Nowhere vanishing one-forms and fibrations over abelian varieties
Abstract: A result of Popa and Schnell shows that any holomorphic one-form on a smooth complex projective variety of general type vanishes somewhere. In this talk, we will explore a complementary question: given a variety of intermediate Kodaira dimension, what can we say about the geometry of the variety if it carries a set of g pointwise linearly independent holomorphic one-forms? Our main result is a classification of all such varieties if the Kodaira ``codimension" is equal to g. This is joint work with Ben Church and Feng Hao.
Pre-talk (1:45pm)
Title: A brief introduction to measures of irrationality
Abstract: The classical question of determining which varieties are rational has led to a huge amount of interest and activity. On the other hand, one can consider a complementary perspective - given a smooth projective variety whose nonrationality is known, how "irrational" is it? I will survey what is currently known, with an emphasis on surfaces and open problems.
Title: A brief introduction to measures of irrationality
Abstract: The classical question of determining which varieties are rational has led to a huge amount of interest and activity. On the other hand, one can consider a complementary perspective - given a smooth projective variety whose nonrationality is known, how "irrational" is it? I will survey what is currently known, with an emphasis on surfaces and open problems.