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Simple connectedness of projective varieties

Author: Steven Dale Cutkosky
Journal: Proc. Amer. Math. Soc. 125 (1997), 679-684
MSC (1991): Primary 14F35, 14E20
MathSciNet review: 1363453
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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.

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  • 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
  • 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
  • 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
  • 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
  • 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, Éditeur, 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
  • Robin Hartshorne, Algebraic geometry, Springer-Verlag, New York-Heidelberg, 1977. Graduate Texts in Mathematics, No. 52. MR 0463157
  • Gennady Lyubeznik, Étale cohomological dimension and the topology of algebraic varieties, Ann. of Math. (2) 137 (1993), no. 1, 71–128. MR 1200077, DOI
  • J. P. Murre, Lectures on an introduction to Grothendieck’s theory of the fundamental group, Tata Institute of Fundamental Research, Bombay, 1967. Notes by S. Anantharaman; Tata Institute of Fundamental Research Lectures on Mathematics, No 40. 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

Received by editor(s): September 14, 1995
Additional Notes: Partially supported by NSF
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1997 American Mathematical Society