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arXiv · 2401.16996

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

Romain Branchereau
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Abstract

Let $V$ be quadratic space of even dimension and of signature $(p, q)$ with $p \geq q > 0$. 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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Romain Branchereau. 2024-01-30. Kudla-Millson lift of toric cycles and restriction of Hilbert modular forms. https://doi.org/10.1007/s00209-025-03683-0

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