Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Polar classes and Segre classes on singular projective varieties
HTML articles powered by AMS MathViewer

by Shoji Yokura PDF
Trans. Amer. Math. Soc. 298 (1986), 169-191 Request permission

Abstract:

We investigate the relation between polar classes of complex varieties and the Segre class of $K$. Johnson [Jo]. Results are obtained for hypersurfaces of projective spaces and for certain varieties with isolated singularities.
References
    A. Dubson, Calcul des invariants numeriques des singularités et applications, S.T.B. Theor. Math., Universität Bonn, 1981. M. Eger, Sur les systèmes canoniques d’une variété algébrique, C. R. Acad. Sci. Paris. Sér. I Math. 204 (1937), 217-219.
  • William Fulton, Rational equivalence on singular varieties, Inst. Hautes Études Sci. Publ. Math. 45 (1975), 147–167. MR 404257
  • William Fulton, On the fundamental group of the complement of a node curve, Ann. of Math. (2) 111 (1980), no. 2, 407–409. MR 569076, DOI 10.2307/1971204
    • —, Introduction to intersection theory in algebraic geometry, Lecture notes prepared for NSF-CBMS Regional Conf. on Intersection Theory in Algebraic Geometry, George Mason Univ., June 27-July 1, 1983.
  • William Fulton, Intersection theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 2, Springer-Verlag, Berlin, 1984. MR 732620, DOI 10.1007/978-3-662-02421-8
  • William Fulton and Dan Laksov, Residual intersections and the double point formula, Real and complex singularities (Proc. Ninth Nordic Summer School/NAVF Sympos. Math., Oslo, 1976) Sijthoff and Noordhoff, Alphen aan den Rijn, 1977, pp. 171–177. MR 0569684
  • William Fulton and Robert MacPherson, Intersecting cycles on an algebraic variety, Real and complex singularities (Proc. Ninth Nordic Summer School/NAVF Sympos. Math., Oslo, 1976) Sijthoff and Noordhoff, Alphen aan den Rijn, 1977, pp. 179–197. MR 0569045
  • William Fulton and Robert MacPherson, Defining algebraic intersections, Algebraic geometry (Proc. Sympos., Univ. Tromsø, Tromsø, 1977) Lecture Notes in Math., vol. 687, Springer, Berlin, 1978, pp. 1–30. MR 527228
  • Phillip Griffiths and Joseph Harris, Principles of algebraic geometry, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York, 1978. MR 507725
  • Gerardo González-Sprinberg, L’obstruction locale d’Euler et le théorème de MacPherson, The Euler-Poincaré characteristic (French), Astérisque, vol. 83, Soc. Math. France, Paris, 1981, pp. 7–32 (French). MR 629121
  • Audun Holme, Embedding obstruction for smooth, projective varieties. I, Studies in algebraic topology, Adv. in Math. Suppl. Stud., vol. 5, Academic Press, New York-London, 1979, pp. 39–67. MR 527244
  • Audun Holme, Embedding-obstruction for singular algebraic varieties in $\textbf {P}^{N}$, Acta Math. 135 (1975), no. 3-4, 155–185. MR 437534, DOI 10.1007/BF02392018
  • Audun Holme and Joel Roberts, Pinch-points and multiple locus of generic projections of singular varieties, Adv. in Math. 33 (1979), no. 3, 212–256. MR 546294, DOI 10.1016/0001-8708(79)90011-2
  • Kent W. Johnson, Immersion and embedding of projective varieties, Acta Math. 140 (1978), no. 1-2, 49–74. MR 463161, DOI 10.1007/BF02392303
  • Steven L. Kleiman, The enumerative theory of singularities, Real and complex singularities (Proc. Ninth Nordic Summer School/NAVF Sympos. Math., Oslo, 1976) Sijthoff and Noordhoff, Alphen aan den Rijn, 1977, pp. 297–396. MR 0568897
  • S. L. Kleiman and Dan Laksov, Schubert calculus, Amer. Math. Monthly 79 (1972), 1061–1082. MR 323796, DOI 10.2307/2317421
  • Lê Dũng Tráng and Bernard Teissier, Variétés polaires locales et classes de Chern des variétés singulières, Ann. of Math. (2) 114 (1981), no. 3, 457–491 (French). MR 634426, DOI 10.2307/1971299
  • R. D. MacPherson, Chern classes for singular algebraic varieties, Ann. of Math. (2) 100 (1974), 423–432. MR 361141, DOI 10.2307/1971080
  • Ragni Piene, Polar classes of singular varieties, Ann. Sci. École Norm. Sup. (4) 11 (1978), no. 2, 247–276. MR 510551
    • —, Cycles polaires et classes de Chern, Séminaire du les singularités des surfaces, 1977-1978, Ecole Polytéchnique, Palaiseau, France, pp. 1-26. J. P. Serre, Algèbre locale—multiplicités, Lecture Notes in Math., vol. 11, Springer-Verlag, Berlin and New York, 1965.
  • Theodore Shifrin, The kinematic formula in complex integral geometry, Trans. Amer. Math. Soc. 264 (1981), no. 2, 255–293. MR 603763, DOI 10.1090/S0002-9947-1981-0603763-8
    • J. A. Todd, The arithmetical invariants of algebraic loci, Proc. London Math. Soc. 43 (1937), 190-225.
  • J. A. Todd, Invariant and covariant systems on an algebraic variety, Proc. London Math. Soc. (2) 46 (1940), 199–230. MR 2214, DOI 10.1112/plms/s2-46.1.199
  • Tohsuke Urabe, Duality of numerical characters of polar loci, Publ. Res. Inst. Math. Sci. 17 (1981), no. 2, 331–345. MR 642646, DOI 10.2977/prims/1195185259
  • Tohsuke Urabe, Generalized Plücker formulae, Publ. Res. Inst. Math. Sci. 17 (1981), no. 2, 347–362. MR 642647, DOI 10.2977/prims/1195185260
  • Hassler Whitney, Complex analytic varieties, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1972. MR 0387634
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 14C15, 14N10
  • Retrieve articles in all journals with MSC: 14C15, 14N10
Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 298 (1986), 169-191
  • MSC: Primary 14C15; Secondary 14N10
  • DOI: https://doi.org/10.1090/S0002-9947-1986-0857438-5
  • MathSciNet review: 857438