Speaker: Hossein Movasati
Date: 10:30 13/01/2023
Title: On a Hodge locus I

Abstract:  Despite the abundant examples of Hodge cycles in the literature, finding them for smooth hypersurfaces of even dimension n is extremely difficult (of course if you do not pick up an algebraic cycle). In this talk I will describe a computer assisted project in order detect instances in which the deformation space of an algebraic Hodge cycle inside a hypersurface is larger than the deformation space of the expected algebraic cycle. One easy example is a Veronese algebraic cycle inside a cubic six fold. A more difficult and conjectural example is an algebraic Hodge cycle which is the sum of two projective spaces of dimension n/2 (lines for n=2 and planes for n=4) inside a Fermat cubic n-fold. The talk is based on Chapter 19 of my book "A Course in Hodge Theory: with Emphasis on Multiple Integrals" which is also available in arXiv:1902.00831.