The Kudla-Millson lift of Siegel cusp forms

Autor:	Kiefer, Paul, Zuffetti, Riccardo
Rok vydání:	2023
Předmět:	Mathematics - Number Theory Mathematics - Algebraic Geometry 11F27 11F37 11F55 14G35
Druh dokumentu:	Working Paper
Popis:	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 that if L splits off two hyperbolic planes and is of sufficiently large rank, then the lift is injective. As an application, we deduce that the image of the lift in the degree 4 cohomology of the associated orthogonal Shimura variety has the same dimension as the lifted space of cusp forms. Our results also cover the case of moduli spaces of quasi-polarized K3 surfaces. To prove the injectivity, we introduce vector-valued indefinite Siegel theta functions of genus 2 and of Jacobi type attached to L. We describe their behavior with respect to the split of a hyperbolic pane in L. This generalizes results of Borcherds to genus higher than 1. Comment: 65 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2307.15809 Zobrazit plný text záznamu View this record from Arxiv