Kudla-Millson lift of toric cycles and restriction of Hilbert modular forms

2024/01/30 by Romain Branchereau, Branchereau, Romain · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2401.16996

openalex publication_date 2024/01/30 · openalex created_date 2024/02/01 · openalex updated_date 2026/07/28

Abstract

Let V be quadratic space of even dimension and of signature (p, q) with p ≥ q > 0. We show that the Kudla-Millson lift of toric cycles - attached to algebraic tori - is a cusp form that is the diagonal restriction of a Hilbert modular form of parallel weight one. We deduce a formula relating the dimension of the span of such diagonal restrictions and the dimension of the span of toric and special cycles.

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