Symmetric powers of symmetric bilinear forms, homogeneous orthogonal polynomials on the sphere and an application to compact Hyperkähler manifolds

DOI10.1142/S0219199716500073zbMath1374.14005arXiv1507.00157MaRDI QIDQ2974067

Simon Kapfer

Publication date: 6 April 2017

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.00157

zbMATH Keywords

spherical harmonicsorthogonal polynomials in several variablesGegenbauer polynomialsHermite polynomialsHankel matricesultraspherical polynomialshyperkähler manifoldsBeauville-Bogomolov formhomogeneous orthogonal polynomialsBeauville-Fujiki relationirreducible holomorphically symplectic manifoldssymmetric bilinear forms on symmetric powers

Mathematics Subject Classification ID

Kähler manifolds (32Q15) Parametrization (Chow and Hilbert schemes) (14C05) Quadratic and bilinear forms, inner products (15A63) Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable (33C50)

Uses Software

• HilbK3

Cites Work

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• Calabi-Yau manifolds and related geometries. Lectures at a summer school in Nordfjordeid, Norway, June 2001
• How to Integrate a Polynomial over a Sphere
• Computing cup products in integral cohomology of Hilbert schemes of points on K3 surfaces
• Classical Algebraic Geometry
• Symmetric Powers of Symmetric Bilinear Forms
• Smith theory and irreducible holomorphic symplectic manifolds

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