Calculations of the Hirzebruch χ_y genera of symmetric products by the holomorphic Lefschetz formula

1999/10/05 by Jian Zhou, Zhou, Jian
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.math/9910029

arxiv created 1999/10/05 · arxiv updated 2009/11/30

Abstract

We calculate the Hirzebruch χ_y and χ_y-genera of symmetric products of closed complex manifolds by the holomorphic Lefschetz formula of Atiyah and Singer \citeAti-Sin. Such calculation rederive some formulas proved in an earlier paper \citeZho by a different method.

Related

• Characteristic classes of symmetric products of complex quasi-projective varieties
• The Hirzebruch genera of complete intersections
• Dold indices and symmetric powers
• Symmetric products of surfaces; a unifying theme for topology and physics
• A Riemann-Roch-Hirzebruch formula for traces of differential operators