Residues in toric varieties
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 resid...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0010437X_v108_n1_p35_Cattani |
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todo:paper_0010437X_v108_n1_p35_Cattani2023-10-03T14:09:03Z Residues in toric varieties Cattani, E. Cox, D. Dickenstein, A. Ample divisors Global Transformation Law Homogeneous ideals Orbifolds Residual currents Residues Toric residues Toric varieties 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0010437X_v108_n1_p35_Cattani |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Ample divisors Global Transformation Law Homogeneous ideals Orbifolds Residual currents Residues Toric residues Toric varieties |
| spellingShingle |
Ample divisors Global Transformation Law Homogeneous ideals Orbifolds Residual currents Residues Toric residues Toric varieties Cattani, E. Cox, D. Dickenstein, A. Residues in toric varieties |
| topic_facet |
Ample divisors Global Transformation Law Homogeneous ideals Orbifolds Residual currents Residues Toric residues Toric varieties |
| description |
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. |
| format |
JOUR |
| author |
Cattani, E. Cox, D. Dickenstein, A. |
| author_facet |
Cattani, E. Cox, D. Dickenstein, A. |
| author_sort |
Cattani, E. |
| title |
Residues in toric varieties |
| title_short |
Residues in toric varieties |
| title_full |
Residues in toric varieties |
| title_fullStr |
Residues in toric varieties |
| title_full_unstemmed |
Residues in toric varieties |
| title_sort |
residues in toric varieties |
| url |
http://hdl.handle.net/20.500.12110/paper_0010437X_v108_n1_p35_Cattani |
| work_keys_str_mv |
AT cattanie residuesintoricvarieties AT coxd residuesintoricvarieties AT dickensteina residuesintoricvarieties |
| _version_ |
1782027325525721088 |