Algebraic Geometry Seminar
Izzet Coskun
UIC
Realizable classes in Grassmannians
Abstract: Given a class in the cohomology of a projective manifold, one can ask whether the class can be represented by an irreducible subvariety. If the class is represented by an irreducible subvariety, we say that the class is realizable. One can further ask whether the subvariety can be taken to satisfy additional properties such as smooth, nondegenerate, rational, etc. These questions are closely related to central problems in algebraic geometry such as the Hodge Conjecture or the Hartshorne Conjecture. Recently, June Huh and collaborators have made significant progress in understanding realizable classes in products of projective spaces. In this talk, I will give a survey of this circle of ideas and discuss recent joint work with Julius Ross on realizable classes in Grassmannians.
Monday September 29, 2025 at 3:00 PM in 636 SEO