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Abstract:

We study residues on a complete toric variety X, which are defined in terms of the homogeneous coordinate ring of X. We first prove a global transformation law for toric residues. When the fan of the toric variety has a simplicial cone of maximal dimension, we can produce an element with toric residue equal to 1. We also show that in certain situations, the toric residue is an isomorphism on an appropriate graded piece of the quotient ring. When X is simplicial, we prove that the toric residue is a sum of local residues. In the case of equal degrees, we also show how to represent X as a quotient (Y\\{0})/C* such that the toric residue becomes the local residue at 0 in Y.

Registro:

Documento: Artículo
Título:Residues in toric varieties
Autor:Cattani, E.; Cox, D.; Dickenstein, A.
Filiación:Dept. of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003, United States
Dept. of Math. and Computer Science, Amherst College, Amherst, MA 01002, United States
Departamento de Matemática, F.C.E. y N., Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Palabras clave:Ample divisors; Global Transformation Law; Homogeneous ideals; Orbifolds; Residual currents; Residues; Toric residues; Toric varieties
Año:1997
Volumen:108
Número:1
Página de inicio:35
Página de fin:76
DOI: http://dx.doi.org/10.1023/A:1000180417349
Título revista:Compositio Mathematica
Título revista abreviado:Compos. Math.
ISSN:0010437X
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0010437X_v108_n1_p35_Cattani

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Citas:

---------- APA ----------
Cattani, E., Cox, D. & Dickenstein, A. (1997) . Residues in toric varieties. Compositio Mathematica, 108(1), 35-76.
http://dx.doi.org/10.1023/A:1000180417349
---------- CHICAGO ----------
Cattani, E., Cox, D., Dickenstein, A. "Residues in toric varieties" . Compositio Mathematica 108, no. 1 (1997) : 35-76.
http://dx.doi.org/10.1023/A:1000180417349
---------- MLA ----------
Cattani, E., Cox, D., Dickenstein, A. "Residues in toric varieties" . Compositio Mathematica, vol. 108, no. 1, 1997, pp. 35-76.
http://dx.doi.org/10.1023/A:1000180417349
---------- VANCOUVER ----------
Cattani, E., Cox, D., Dickenstein, A. Residues in toric varieties. Compos. Math. 1997;108(1):35-76.
http://dx.doi.org/10.1023/A:1000180417349