2020/09/08 by Małgorzata Mikosz, Andrzej Weber
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models
paper · pdf · doi:10.1007/s10801-020-00938-3
openalex publication_date 2020/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
Abstract We revisit the construction of elliptic class given by Borisov and Libgober for singular algebraic varieties. Assuming torus action we adjust the theory to the equivariant local situation. We study theta function identities having a geometric origin. In the case of quotient singularities \mathbb Cn/G <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> <mml:mo>/</mml:mo> <mml:mi>G</mml:mi> </mml:mrow> </mml:math> , where G is a finite group the theta identities arise from McKay correspondence. The symplectic singularities are of special interest. The Du Val surface singularity An <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>A</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:math> leads to a remarkable formula.