The Chow ring of a singular surface

J. G. Biswas; V. Srinivas

doi:10.1007/BF02844480

The Chow ring of a singular surface

J. G. Biswas
, V. Srinivas

Mathematics

Tata Institute of Fundamental Research

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We construct the Chow ring CH*(X) = CH⁰(X)⊕CH¹(X)⊕ CH²(X) of a reduced, quasi-projective surface X, together with Chern class maps c_i : K₀(X) → CHⁱ (X), with the usual properties. As a consequence, we show that the cycle map CH²(X) → F₀K₀(X) is an isomorphism. Our treatment is greatly influenced by an unpublished 1983 preprint of Levine's, but is much simpler, since we deal only with surfaces.

Original language	English
Pages (from-to)	227-249
Number of pages	23
Journal	Proceedings of the Indian Academy of Sciences: Mathematical Sciences
Volume	108
Issue number	3
DOIs	https://doi.org/10.1007/BF02844480
State	Published - Oct 1998

Keywords

Chern class maps
Chow ring
Singular surface

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10.1007/BF02844480

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title = "The Chow ring of a singular surface",

abstract = "We construct the Chow ring CH*(X) = CH0(X)⊕CH1(X)⊕ CH2(X) of a reduced, quasi-projective surface X, together with Chern class maps ci : K0(X) → CHi (X), with the usual properties. As a consequence, we show that the cycle map CH2(X) → F0K0(X) is an isomorphism. Our treatment is greatly influenced by an unpublished 1983 preprint of Levine's, but is much simpler, since we deal only with surfaces.",

keywords = "Chern class maps, Chow ring, Singular surface",

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year = "1998",

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T1 - The Chow ring of a singular surface

AU - Biswas, J. G.

AU - Srinivas, V.

PY - 1998/10

Y1 - 1998/10

N2 - We construct the Chow ring CH*(X) = CH0(X)⊕CH1(X)⊕ CH2(X) of a reduced, quasi-projective surface X, together with Chern class maps ci : K0(X) → CHi (X), with the usual properties. As a consequence, we show that the cycle map CH2(X) → F0K0(X) is an isomorphism. Our treatment is greatly influenced by an unpublished 1983 preprint of Levine's, but is much simpler, since we deal only with surfaces.

AB - We construct the Chow ring CH*(X) = CH0(X)⊕CH1(X)⊕ CH2(X) of a reduced, quasi-projective surface X, together with Chern class maps ci : K0(X) → CHi (X), with the usual properties. As a consequence, we show that the cycle map CH2(X) → F0K0(X) is an isomorphism. Our treatment is greatly influenced by an unpublished 1983 preprint of Levine's, but is much simpler, since we deal only with surfaces.

KW - Chern class maps

KW - Chow ring

KW - Singular surface

UR - https://www.scopus.com/pages/publications/0011605094

U2 - 10.1007/BF02844480

DO - 10.1007/BF02844480

M3 - Article

AN - SCOPUS:0011605094

SN - 0253-4142

VL - 108

SP - 227

EP - 249

JO - Proceedings of the Indian Academy of Sciences: Mathematical Sciences

JF - Proceedings of the Indian Academy of Sciences: Mathematical Sciences

IS - 3

ER -

The Chow ring of a singular surface

Abstract

Keywords

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