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Torus embeddings, polyhedra, k*-actions and homology

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Jurkiewicz J.

Instytut Matematyczny Polskiej Akademii Nauk

EN

CONTENTS Introduction..............................................................................................5 1. General torus embeddings...................................................................7 1.1. Sets of subrings..............................................................................7 1.2. Complex of cones and torus embeddings. Basic properties and notation...............8 1.3. Jets of 1-p.s. at 0...........................................................................12 1.4. An application of torus embeddings. Desigularization of plane cusps by blowings up of the plane...............14 1.5. Some $G_m$-actions on torus embedding...................................18 2. Complex torus embeddings. Real and lion-negative parts..................20 2.1. Introduction...................................................................................20 2.2. The real non-negative part of the variety $X_Σ$...........................21 2.3. Bijection of $X_σ^{≥0}$ onto σ̆......................................................29 2.4. Real part of $X_Σ$. Reflexions......................................................35 3. Projective torus embeddings..............................................................37 3.1. Polyhedra......................................................................................37 3.2. Morse function...............................................................................41 3.3. Filtrations, cycles of orbits and projectivity.....................................46 4. Homology............................................................................................50 4.1. Poincaré polynomial......................................................................50 4.2. Chow ring and l-adic cohomology..................................................51 4.3. Cohomology ring of $X_Σ(R)$ with coefficients in Z/2Z..................52 4.4. Orientation.....................................................................................55 4.5. The 2-dimensional case, homology with integral coefficients.........56 References.............................................................................................62 Index.......................................................................................................64

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Correction to "Corrections to the paper «A remark on the orbit spaces under multiplicative group actions»" (Colloquium Mathematicum 57.2 (1989), pp. 361--362)

96%

Jurkiewicz J.

Colloquium Mathematicum

|

1990

|

tom 59

|

nr 2

297

3

Review: Effective Methods in Algebraic Geometry - Edited by T. Mora, C. Traverso

61%

Jurkiewicz J., Rempała J.

Mathematica Applicanda

|

1993

|

tom 22

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nr 36

PL

Artykuł nie zawiera streszczenia

EN

The article contains no abstract

4

Corrections to the paper "A remark on the orbit spaces under multiplicative group actions''

60%

Jurkiewicz J.

Colloquium Mathematicum

|

1989

|

tom 57

|

nr 2

361-362

5

A remark on the orbit spaces under multiplicative group actions

42%

Jurkiewicz J.

Colloquium Mathematicum

|

1987

|

tom 54

|

nr 1

67-70

Ograniczanie wyników

3 Colloquium Mathematicum

1 Mathematica Applicanda

5 Jurkiewicz J.

1 Rempała J.

1 1993

1 1990

1 1989

1 1987

1 1985

Torus embeddings, polyhedra, k*-actions and homology

Correction to "Corrections to the paper «A remark on the orbit spaces under multiplicative group actions»" (Colloquium Mathematicum 57.2 (1989), pp. 361--362)

Review: Effective Methods in Algebraic Geometry - Edited by T. Mora, C. Traverso

Corrections to the paper "A remark on the orbit spaces under multiplicative group actions''

A remark on the orbit spaces under multiplicative group actions