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 for 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.

algebraic geometrycombinatorics

Audience: researchers in the topic

Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html