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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Simple connectedness of projective varieties
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by Steven Dale Cutkosky PDF
Proc. Amer. Math. Soc. 125 (1997), 679-684 Request permission

Abstract:

A Lefschetz type theorem is proven relating the algebraic fundamental group of a smooth projective variety $X$ to the algebraic fundamental group of a subvariety set theoretically defined by $\le \dim (X)-2$ forms.
References
  • Oscar Zariski, The theorem of Riemann-Roch for high multiples of an effective divisor on an algebraic surface, Ann. of Math. (2) 76 (1962), 560–615. MR 141668, DOI 10.2307/1970376
  • Steven Dale Cutkosky and Hema Srinivasan, Local fundamental groups of surface singularities in characteristic $p$, Comment. Math. Helv. 68 (1993), no. 2, 319–332. MR 1214235, DOI 10.1007/BF02565822
  • S.D. Cutkosky, Purity of branch locus and Lefschetz theorems, Compositio Math. 96, (1995) 173-195.
  • Gerd Faltings, Algebraisation of some formal vector bundles, Ann. of Math. (2) 110 (1979), no. 3, 501–514. MR 554381, DOI 10.2307/1971235
  • Mark Goresky and Robert MacPherson, Stratified Morse theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 14, Springer-Verlag, Berlin, 1988. MR 932724, DOI 10.1007/978-3-642-71714-7
  • A. Grothendieck, ÉlĂ©ments de gĂ©omĂ©trie algĂ©brique. III. Étude cohomologique des faisceaux cohĂ©rents. II, Inst. Hautes Études Sci. Publ. Math. 17 (1963), 91 (French). MR 163911
  • RevĂȘtements Ă©tales et groupe fondamental, Lecture Notes in Mathematics, Vol. 224, Springer-Verlag, Berlin-New York, 1971 (French). SĂ©minaire de GĂ©omĂ©trie AlgĂ©brique du Bois Marie 1960–1961 (SGA 1); DirigĂ© par Alexandre Grothendieck. AugmentĂ© de deux exposĂ©s de M. Raynaud. MR 0354651
  • Alexander Grothendieck, Cohomologie locale des faisceaux cohĂ©rents et thĂ©orĂšmes de Lefschetz locaux et globaux $(SGA$ $2)$, North-Holland Publishing Co., Amsterdam; Masson & Cie, Editeur, Paris, 1968 (French). AugmentĂ© d’un exposĂ© par MichĂšle Raynaud; SĂ©minaire de GĂ©omĂ©trie AlgĂ©brique du Bois-Marie, 1962; Advanced Studies in Pure Mathematics, Vol. 2. MR 0476737
  • Helmut A. Hamm, Lefschetz theorems for singular varieties, Singularities, Part 1 (Arcata, Calif., 1981) Proc. Sympos. Pure Math., vol. 40, Amer. Math. Soc., Providence, RI, 1983, pp. 547–557. MR 713091, DOI 10.1007/bf00118520
  • Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. MR 0463157, DOI 10.1007/978-1-4757-3849-0
  • Gennady Lyubeznik, Étale cohomological dimension and the topology of algebraic varieties, Ann. of Math. (2) 137 (1993), no. 1, 71–128. MR 1200077, DOI 10.2307/2946619
  • J. P. Murre, Lectures on an introduction to Grothendieck’s theory of the fundamental group, Tata Institute of Fundamental Research Lectures on Mathematics, No. 40, Tata Institute of Fundamental Research, Bombay, 1967. Notes by S. Anantharaman. MR 0302650
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Additional Information
  • Steven Dale Cutkosky
  • Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
  • MR Author ID: 53545
  • ORCID: 0000-0002-9319-0717
  • Email: dale@cutkosky.math.missouri.edu
  • Received by editor(s): September 14, 1995
  • Additional Notes: Partially supported by NSF
  • Communicated by: Wolmer V. Vasconcelos
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 679-684
  • MSC (1991): Primary 14F35, 14E20
  • DOI: https://doi.org/10.1090/S0002-9939-97-03658-7
  • MathSciNet review: 1363453