Lefschetz decompositions of Kudla-Millson theta functions

Autor:	Bruinier, Jan Hendrik, Zuffetti, Riccardo
Rok vydání:	2024
Předmět:	Mathematics - Number Theory Mathematics - Algebraic Geometry 11F27 (Primary) 14J10 11F46 14C25 (Secondary)
Druh dokumentu:	Working Paper
Popis:	In the 80'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 form on an orthogonal Shimura variety with respect to the other variable. We prove that the Lefschetz decomposition of the cohomology class of that theta function is also its modular decomposition in Eisenstein, Klingen and cuspidal parts. We also show that the image of the Kudla-Millson lift is contained in the primitive cohomology of X. As an application, we deduce dimension formulas for the cohomology of X in low degree. Our results cover the cases of moduli spaces of compact hyperk\"ahler manifolds. Comment: 34 pages, comments are welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2406.19921 Zobrazit plný text záznamu View this record from Arxiv