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A Barth-type theorem for branched coverings of projective space. (English) Zbl 0434.32013


MSC:

32C35 Analytic sheaves and cohomology groups
14E20 Coverings in algebraic geometry
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14E25 Embeddings in algebraic geometry
32J25 Transcendental methods of algebraic geometry (complex-analytic aspects)
32H99 Holomorphic mappings and correspondences

Citations:

Zbl 0206.500
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References:

[1] Barth, W.: Transplanting cohomology classes in complex-projective space. Amer. J. Math.92, 951-967 (1970) · Zbl 0206.50001 · doi:10.2307/2373404
[2] Barth, W.: Larsen’s theorem on the homotopy groups of projective manifolds of small embedding codimension. Proc. Symp. Pure Math.29, 307-313 (1975) · Zbl 0309.14017
[3] Berstein, I., Edmonds, A.: The degree and branch set of a branched covering. Invent. Math.45, 213-220 (1978) · Zbl 0365.55001 · doi:10.1007/BF01403169
[4] Bloch, S., Gieseker, D.: The positivity of the Chern classes of an ample vector bundle. Invent. Math.12, 112-117 (1971) · Zbl 0212.53502 · doi:10.1007/BF01404655
[5] Deligne, P.: Letter to W. Fulton, 18 Nov. 1979
[6] Fulton, W.: Notes on connectivity in algebraic geometry (preprint)
[7] Fulton, W., Hansen, J.: A connectedness theorem for projective varieties, with applications to intersections and singularities of mappings. Ann. of Math.110, 159-166 (1979) · Zbl 0405.14012 · doi:10.2307/1971249
[8] Gaffney, T., Lazarsfeld, R.: On the ramification of branched coverings of IP n . Invent. Math. (to appear) · Zbl 0422.14010
[9] Hartshorne, R.: Ample vector bundles. Publ. Math. IHES29, 63-94 (1966) · Zbl 0173.49003
[10] Hartshorne, R.: Varieties of small codimension in projective space. Bull. AMS80, 1017-1032 (1974) · Zbl 0304.14005 · doi:10.1090/S0002-9904-1974-13612-8
[11] Hartshorne, R.: Equivalence relations on algebraic cycles and subvarieties of small codimension. Proc. Symp. Pure Math.29, 129-164 (1975) · Zbl 0314.14001
[12] Hartshorne, R.: Algebraic geometry. In: Graduate Texts in Mathematics 52. Berlin, Heidelberg, New York: Springer 1977 · Zbl 0367.14001
[13] Larsen, M.: On the topology of complex projective manifolds. Invent. Math.19, 251-260 (1973) · Zbl 0255.32004 · doi:10.1007/BF01390209
[14] Lazarsfeld, R.: Thesis, Brown University 1980
[15] Mumford, D.: Lectures on curves on an algebraic surface. Ann. of Math. Stud.59 (1966) · Zbl 0187.42701
[16] Mumford, D.: Algebraic geometry. I. complex projective varieties. In: Grundlehren der mathematischen Wissenschaften, Vol. 221, Berlin, Heidelberg, New York: Springer 1976 · Zbl 0356.14002
[17] Sommese, A.: Submanifolds of abelian varieties. Math. Ann.233, 229-256 (1978) · Zbl 0381.14007 · doi:10.1007/BF01405353
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