6 papers
The Siegel-Weil formula in geometry and arithmetic
Jan Hendrik Bruinier, Riccardo Zuffetti
The present paper is an extended version of the lecture notes of a course given by the first author at the summer school on Formulas of Siegel and Weil (Bielefeld, September 2025).…
Extremal divisors on moduli spaces of K3 surfaces
Ignacio Barros, Laure Flapan, Riccardo Zuffetti
We establish criteria for when Noether--Lefschetz divisors generate an extremal ray in the cone of pseudoeffective divisors of an orthogonal modular variety. In particular, we exhi…
The Kudla-Millson lift of Siegel cusp forms
Paul Kiefer, Riccardo Zuffetti
We study the injectivity of the Kudla-Millson lift of genus 2 Siegel cusp forms, vector-valued with respect to the Weil representation associated to an even lattice L. We prove tha…
Injectivity of the genus 1 Kudla-Millson lift on locally symmetric spaces
Ingmar Metzler, Riccardo Zuffetti
Let be an even indefinite lattice. We show that if splits off a hyperbolic plane and a scaled hyperbolic plane, then the Kudla-Millson lift of genus associated to i…
Cones of orthogonal Shimura subvarieties and equidistribution
Riccardo Zuffetti
Let X be an orthogonal Shimura variety, and let C_r(X) be the cone generated by the cohomology classes of orthogonal Shimura subvarieties in X of dimension r. We investigate the as…
Lefschetz decompositions of Kudla-Millson theta functions
Jan Hendrik Bruinier, Riccardo Zuffetti
In the 1980's Kudla and Millson introduced a theta function in two variables. It behaves as a Siegel modular form with respect to the first variable, and is a closed differential f…