Gusein-Zade, Sabir Medgidovich and Luengo Velasco, Ignacio and Melle Hernández, Alejandro (2006) Power structure over the Grothendieck ring of varieties and generating series of Hilbert schemes of points. Michigan Mathematical Journal, 54 (2). pp. 353-359. ISSN 0026-2285
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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.
The first author was partially supported by the grants RFBR-04-01-00762, NSh-1972.2003.1. The last two authors were partially supported by the grant BFM2001-1488-C02-01.
|Uncontrolled Keywords:||Surface; Plane|
|Subjects:||Sciences > Mathematics > Algebraic geometry|
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|Deposited On:||03 Oct 2012 08:18|
|Last Modified:||07 Feb 2014 09:32|
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