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<p>Let <i>V</i> be quadratic space of even dimension and of signature (<i>p</i>,&#xa0;<i>q</i>) with <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="209_2025_3683_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="73" /> </InlineMediaObject> <EquationSource Format="TEX">\(p \ge q&gt;0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>≥</mo> <mi>q</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>. We show that the Kudla-Millson lift of <i>toric</i> 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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年2月12日

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  • Romain Branchereau

摘要

Let V be quadratic space of even dimension and of signature (p, q) with \(p \ge q>0\) 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.