RT Journal Article
T1 A power structure over the Grothendieck ring of varieties
A1 Gusein-Zade, Sabir Medgidovich
A1 Luengo Velasco, Ignacio
A1 Melle Hernández, Alejandro
AB 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.
PB International Press
SN 1073-2780
YR 2004
FD 2004
LK https://hdl.handle.net/20.500.14352/50128
UL https://hdl.handle.net/20.500.14352/50128
LA eng
NO The authors are thankful to Tomás L. Gómez for useful discussions. Partially supported by the grants RFBR–01–01–00739, INTAS–00–259, NWO–RFBR–047.008.005. The last two authors were partially supported by the grant BFM2001–1488–C02–01.
DS Docta Complutense
RD 10 abr 2025