Power structure over the Grothendieck ring of varieties and generating series of Hilbert schemes of points

By Sabir M. Gusein-Zade, Ignacio Luengo, Alejandro Melle-Hernández. 2004

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The power structure over the Grothendieck (semi)ring of complex quasi-projective varieties constructed by the authors is used to express the generating series of classes of Hilbert schemes of zero-dimensional subschemes on a smooth quasi-projective variety as an exponent of that for the complex affine space of the same dimension. Specializations of this relation give formulae for generating series of such invariants of the Hilbert schemes of points as the Euler characteristic and the Hodge-Deligne polynomial.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4255a150e83937ef489cb4e4eeb71e6736021605

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In Algebra and Number Theory

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Motivic degree zero Donaldson–Thomas invariants (2009, methodology): “The now standard technology [6, 15, 17, 13] allows us to express in Theorem 3.”