Geometry Seminar

University of Tor Vergata, Department of Mathematics

17th of January 2023, 14:30-15:30, room “Dal Passo”

Speaker

Maria Gioia Cifanai

(Roma Tre)

Title

Reconstructing curves from their Hodge classes

Abstract

Recently, Movasati and Sertöz pose several interesting questions about the reconstruction of a variety from its Hodge class. In particular they give the notion of a perfect class: the Hodge class of a variety X is perfect if its annihilator is a sum of ideals of varieties whose Hodge class is a nonzero rational multiple of that of X. I will report on a joint work with Gian Pietro Pirola and Enrico Schlensiger, in which we give an answer to some of these questions fot curves: in particular, we show that the Hodge class of a smooth rational quartic on a surface of degree 4 is not perfect, and that the Hodge class of an arithmetically Cohen-Macaulay curve is always perfect. Moreover, I will give some results on the problem in higher dimension.