Torus embeddings, polyhedra, k*-actions and homology

Jerzy Jurkiewicz

GDML_Books, (1985), p.

Résumé

CONTENTSIntroduction..............................................................................................51. 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...................................182. 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......................................................353. Projective torus embeddings..............................................................37  3.1. Polyhedra......................................................................................37  3.2. Morse function...............................................................................41  3.3. Filtrations, cycles of orbits and projectivity.....................................464. 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.........56References.............................................................................................62Index.......................................................................................................64

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Zbl 0599.14014

EUDML-ID : urn:eudml:doc:268485