Algebraic Geometry Seminar: "Hodge cycles for cubic hypersurfaces"
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 consider the Hodge/algebraic cycle which is the sum of two projective space of dimension n/2 (lines for n=2 and planes for n=4) and describe a computer assisted project in order detect instances in which the deformation space of such a Hodge cycle inside a hypersurface is larger than the deformation space of the expected algebraic cycle. 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.
Host: Matt Kerr