Lazarsfeld, Robert A Barth-type theorem for branched coverings of projective space. (English) Zbl 0434.32013 Math. Ann. 249, 153-162 (1980). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 5 ReviewsCited in 18 Documents 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 Keywords:projective variety; complex cohomology; finite holomorphic mapping; ample vector bundle; complex projective space; triple covering Citations:Zbl 0206.500 PDFBibTeX XMLCite \textit{R. Lazarsfeld}, Math. Ann. 249, 153--162 (1980; Zbl 0434.32013) Full Text: DOI EuDML 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.