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Título:
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A power structure over the Grothendieck ring of varieties
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Autores:
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Gusein-Zade, Sabir Medgidovich ;
Luengo Velasco, Ignacio ;
Melle Hernández, Alejandro
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Tipo de documento:
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texto impreso
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Editorial:
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International Press, 2004
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Dimensiones:
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application/pdf
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Nota general:
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info:eu-repo/semantics/restrictedAccess
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Idiomas:
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Palabras clave:
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Estado = Publicado
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Materia = Ciencias: Matemáticas: Teoría de números
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Tipo = Artículo
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Resumen:
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Let R be either the Grothendieck semiring (semigroup with multiplication) of complex quasi-projective varieties, or the Grothendieck ring of these varieties, or the Grothendieck ring localized by the class \L of the complex affine line. We define a power structure over these (semi)rings. This means that, for a power series A(t)=1+?i=1?[Ai]ti with the coefficients [Ai] from R and for [M]?R, there is defined a series (A(t))[M], also with coefficients from R, so that all the usual properties of the exponential function hold. In the particular case A(t)=(1?t)?1, the series (A(t))[M] is the motivic zeta function introduced by M. Kapranov. As an application we express the generating function of the Hilbert scheme of points, 0-dimensional subschemes, on a surface as an exponential of the surface.
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En línea:
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https://eprints.ucm.es/id/eprint/16623/1/Luengo10.pdf
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