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1998 | 44 | 1 | 21-35
Tytuł artykułu

On homology classes represented by real algebraic varieties

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Rocznik
Tom
44
Numer
1
Strony
21-35
Opis fizyczny
Daty
wydano
1998
Twórcy
  • Department of Mathematics, Vrije Universiteit, De Boelelaan 1081, 1081 HV - Amsterdam, The Netherlands
  • University of New Mexico, Department of Mathematics and Statistics, Albuquerque, New Mexico 87131-1141, U.S.A.
Bibliografia
  • [1] R. Benedetti and M. Dedò, Counterexamples to representing homology classes by real algebraic subvarieties up to homeomorphism, Compositio Math. 53 (1984), 143-151.
  • [2] R. Benedetti and A. Tognoli, Approximation theorems in real algebraic geometry, Boll. Un. Mat. Ital. Suppl. 1980, no. 2, 209-228.
  • [3] R. Benedetti and A. Tognoli, On real algebraic vector bundles, Bull. Sci. Math. (2) 104 (1980), 89-112.
  • [4] R. Benedetti and A. Tognoli, Remarks and counterexamples in the theory of real algebraic vector bundles and cycles, in: Géométrie algébrique réelle et formes quadratiques, Lecture Notes in Math. 959, Springer, Berlin, 1982, 198-211.
  • [5] E. Bierstone and P. D. Milman, Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant, Invent. Math. 128 (1997), 207-302.
  • [6] J. Bochnak, M. Coste and M.-F. Roy, Géométrie algébrique réelle, Ergeb. Math. Grenzgeb. (3) 12, Springer, Berlin, 1987.
  • [7] J. Bochnak and J. Huisman, When is a complex elliptic curve the product of two real algebraic curves?, Math. Ann. 293 (1992), 469-474.
  • [8] J. Bochnak and W. Kucharz, Algebraic approximation of mappings into spheres, Michigan Math. J. 34 (1987), 119-125.
  • [9] J. Bochnak and W. Kucharz, Algebraic models of smooth manifolds, Invent. Math. 97 (1989), 585-611.
  • [10] J. Bochnak and W. Kucharz, K-theory of real algebraic surfaces and threefolds, Math. Proc. Cambridge Philos. Soc. 106 (1989), 471-480.
  • [11] J. Bochnak and W. Kucharz, Algebraic cycles and approximation theorems in real algebraic geometry, Trans. Amer. Math. Soc. 337 (1993), 463-472.
  • [12] J. Bochnak and W. Kucharz, Real algebraic hypersurfaces in complex projective varieties, Math. Ann. 301 (1995), 381-397.
  • [13] J. Bochnak, W. Kucharz and M. Shiota, The divisor class groups of some rings of global real analytic, Nash or regular functions, in: Géométrie algébrique réelle et formes quadratiques, Lecture Notes in Math. 959, Springer, Berlin, 1982, 218-248.
  • [14] J. Bochnak, W. Kucharz and M. Shiota, On algebraicity of global real analytic sets and functions, Invent. Math. 70 (1982), 115-156.
  • [15] A. Borel and A. Haefliger, La classe d'homologie fondamentale d'un espace analytique, Bull. Soc. Math. France 89 (1961), 461-513.
  • [16] N. Bourbaki, Algèbre commutative, Hermann, Paris, 1961-1965.
  • [17] L. Bröcker, Reelle Divisoren, Arch. Math. (Basel) 35 (1980), 140-143.
  • [18] W. Fulton, Intersection Theory, Ergeb. Math. Grenzgeb. (3) 2, Springer, Berlin, 1984.
  • [19] J. van Hamel, Real algebraic cycles on complex projective varieties, Math. Z. 225 (1997), 177-198.
  • [20] H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero, Ann. of Math. (2) 79 (1964), 109-203, 205-326.
  • [21] S. T. Hu, Homotopy Theory, Academic Press, New York, 1959.
  • [22] J. Huisman, Real abelian varieties with complex multiplication, Ph.D. Thesis, Vrije Universiteit Amsterdam, 1992.
  • [23] J. Huisman, The underlying real algebraic structure of complex elliptic curves, Math. Ann. 294 (1992), 19-35.
  • [24] J. Huisman, A real algebraic vector bundle is strongly algebraic whenever its total space is affine, in: Real Algebraic Geometry and Topology, Contemp. Math. 182, Amer. Math. Soc., Providence, 1995, 117-119.
  • [25] F. Ischebeck and H.-W. Schülting, Rational and homological equivalence for real cycles, Invent. Math. 94 (1988), 307-316.
  • [26] N. Ivanov, Approximation of smooth manifolds by real algebraic sets, Russian Math. Surveys 37 (1982), 1-59.
  • [27] W. Kucharz, On homology of real algebraic sets, Invent. Math. 82 (1985), 19-25.
  • [28] W. Kucharz, Algebraic equivalence and homology classes of real algebraic varieties, Math. Nachr. 180 (1996), 135-140.
  • [29] F. Mangolte, Cycles algébriques sur les surface K3 réelles, Math. Z. 225 (1997), 559-576.
  • [30] F. Mangolte and J. van Hamel, % Algebraic cycles on real Enriques surfaces, %preprint, 1996. Algebraic cycles and topology of real Enriques surfaces, Compositio Math. 110 (1998), 215-237.
  • [31] J.-J. Risler, Sur l'homologie des surfaces algébriques réelles, in: Géométrie algébrique réelle et formes quadratiques, Lecture Notes in Math. 959, Springer, Berlin, 1982, 381-385.
  • [32] H.-W. Schülting, Algebraische und topologische reelle Zyklen unter birationalen Transformationen, Math. Ann. 272 (1985), 441-448.
  • [33] M. Shiota, Real algebraic realization of characteristic classes, Publ. Res. Inst. Math. Sci. 18 (1982), 995-1008.
  • [34] M. Shiota, Equivalence of differentiable functions, rational functions and polynomials, Ann. Inst. Fourier (Grenoble) 32 no. 4 (1982), 167-204.
  • [35] R. Silhol, A bound on the order of $H^(a)_n-1(X,ℤ/2)$ on a real algebraic variety, in: Géométrie algébrique réelle et formes quadratiques, Lecture Notes in Math. 959, Springer, Berlin, 1982, 443-450.
  • [36] R. Silhol, Real Algebraic Surfaces, Lecture Notes in Math. 1392, Springer, Berlin, 1989.
  • [37] P. Teichner, 6-dimensional manifolds without totally algebraic homology, Proc. Amer. Math. Soc. 123 (1995), 2909-2914.
  • [38] R. Thom, Quelques propriétés globales des variétés différentiables, Comment. Math. Helv. 28 (1954), 17-86.
  • [39] A. Tognoli, Su una congettura di Nash, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 27 (1973), 167-185.
  • [40] E. Witt, Zerlegung reeler algebraischer Funktionen in Quadrate, Schiefkörper über reellen Funktionenkörper, J. Reine Angew. Math. 171 (1934), 4-11.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
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