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Tytuł książki

Torus embeddings, polyhedra, k*-actions and homology

Seria
Rozprawy Matematyczne tom/nr w serii: 236 wydano: 1985
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Abstrakty
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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
Słowa kluczowe
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Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 236
Liczba stron
64
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCXXXVI
Daty
wydano
1985
Twórcy
Bibliografia
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  • [B-B₁] A. Białynicki-Birula, Some theorems on actions of algebraic groups, Ann. of Math. 98 (1973), 480-497.
  • [B-B₂] A. Białynicki-Birula, On fixed points of torus action on projective varieties, Bull. Acad. Polon. Sci., Sér. Sci. Math. 22 (1974), 1097-1101.
  • [B-B₃] A. Białynicki-Birula, Some properties of the decomposition of algebraic varieties determined by actions of a torus, Bull. Acad. Polon. Sci., Sér. Sci. Math. 24 (1976), 667-674.
  • [B-S] A. Borel and J-P. Serre, Corners and arithmetic groups. Comment. Math. Helv. 48 (1973).
  • [C-S] J. B. Carrell and A. J. Sommese, Some topological aspects of C*-actions on compact Kähler manifolds, Comment. Math. Helv. 54 (1979), 567-582.
  • [Dan] V. I. Danilov, Geometria toricheskih mnogoobrazii, Uspekhi Mat. Nauk 33 (1978), 85-134.
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  • [E] F. Ehlers, Eine Klasse Komplexer Mannigfaltigkeiten und die Auflösung einiger isolierter Singularitäten, Math. Ann. 218 (1975), 127-156.
  • [F] T. Frankel, Fixed points and torsion on Kähler Manifolds, Ann. of Math. 70 (1959), 1-9.
  • [G] A. Grothendick, Formule de Lefschetz et rationalité des fonctions L, Dix exposés sur la cohomologie des schémas, North-Holland, Amsterdam 1968.
  • [G-S] V. Guillemin, S. Sternberg, Convexity properties of the moment mapping, Inventiones Math. 67 (1982).
  • [H] F. Hirzebruch, Über vierdimensionale Riemannsche Flähen mehrdeutiger analytischer Funktionen von zwei complexen Veränderlichen, Math. Ann. 126 (1953), 1-22.
  • [J₁] J. Jurkiewicz, An example of algebraic torus action which determines the nonfiltrable decomposition, Bull. Acad. Polon. Sci. Sér. Sci Math. 25 (1977), 1089-1092.
  • [J₂] J. Jurkiewicz, Chow ring of projective non-singular torus embedding, Colloq. Math. 43 (1980), 261-270.
  • [J₃] J. Jurkiewicz, On the complex projective torus embedding, the associated variety with corners and Morse functions, Bull. Acad. Polon. Sci. Sér. Sci. Math. 29 (1981), 21-27.
  • [K] J. Konarski, A pathological example of an action of k* in Group Action and Vector Fields, Proceedings, Vancouver 15.01-15.02.1981, Lecture Notes in Math, 956, Springer-Verlag, Berlin 1982.
  • [M] J. W. Milnor, Morse Theory, Ann. of Math. Stud. 51, Princeton Univ. Press, Princeton 1963.
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  • [TE] G. Kempf, F. Knudsen, D. Mumford, B. Saint-Donat, Toroidal embeddings I, Lecture Notes in Math. 339, Springer Verlag, Berlin 1973. All references are to Chapter 1.
  • [TEA] T. Oda, Torus embeddings and applications, Tata Inst. Fund. Res. Studies in Math., Tata Inst. Fundamental Res., Bombay 1978.
  • [W] R. J. Walker, Algebraic Curves, Princeton University Press, Princeton 1950.
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bwmeta1.element.zamlynska-a0403a66-3cf0-49f0-8d8d-8c007d58ab62
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ISBN
83-01-06364-5
ISSN
0012-3862
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