Barth type vanishing theorem

Geometriae Dedicata - Tập 141 - Trang 87-92 - 2008
F. Laytimi1, D. S. Nagaraj2
1Mathématiques-Bât. M2, Villeneuve d’Ascq Cedex, France
2Institute of Mathematical Sciences, C.I.T. Campus, Chennai, India

Tóm tắt

In this paper we give a vanishing result for cohomology groups of symmetric powers of the co-normal bundle of a non-degenerate smooth subvariety X of projective space, then we use this theorem to give a Barth type vanishing theorem.

Tài liệu tham khảo

Alzati A.: Barth type vanishing theorems. Geometrica Dedicata 44, 159–168 (1992) Ein, L.: Vanishing theorem for varieties of low codimension. In: Algebraic Geometry, vol. 1311, pp. 71–75. Springer LNM, Sundance (1986) Peternell Th., Le Potier J., Schneider M.: Vanishing theorem, linear and quadratic normality. Invent. Math. 87, 573–586 (1987) Schneider M., Zintl J.: The theorem of Barth-Lefschetz as a consequence of Le Potier’s vanishing theorem. Manuscripta mathematica 80, 259–263 (1993) Shiffman, B., Sommese, A.J.: Vanishing theorems on complex manifolds. Progr. Math. 56 Birkhäuser (1985) Sommese A.J.: Submanifolds of Abelian varieties. Math. Ann. 233, 229–256 (1978) Zak F.L.: Projections of algebraic varieties. Mat. USSR. Sbornik 44(4), 535–543 (1983)