On injectivity, vanishing and torsion-free theorems for algebraic varieties
Osamu Fujino
Source: Proc. Japan Acad. Ser. A Math. Sci.
Volume 85, Number 8
(2009), 95-100.
Abstract
We give a short and almost self-contained proof of generalizations of Kollár’s vanishing and torsion-free theorems. Although they are contained in Ambro's much more general results on embedded normal crossing pairs, we give an alternate and direct reduction argument to the mixed Hodge theory. In this sense, this paper gives a more readable account of the application to the log minimal model program for log canonical pairs.
Primary Subjects: 14F17, 32L20
Secondary Subjects: 14E30
Keywords: Vanishing theorem; torsion-freeness; injectivity theorem; Hodge theory
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.pja/1254491211
Digital Object Identifier: doi:10.3792/pjaa.85.95
References
F. Ambro, Tr. Mat. Inst. Steklova 240 (2003), Biratsion. Geom. Linein. Sist. Konechno Porozhdennye Algebry, 220--239; translation in Proc. Steklov Inst. Math. 2003, no. 1 (240), 214--233.
P. Deligne, Théorie de Hodge. II, Inst. Hautes Études Sci. Publ. Math. no. 40 (1971), 5--57.
Mathematical Reviews (MathSciNet):
MR498551
H. Esnault and E. Viehweg, Lectures on vanishing theorems, Birkhäuser, Basel, 1992.
O. Fujino, Introduction to the log minimal model program for log canonical pairs. (Preprint).
O. Fujino, Non-vanishing theorem for log canonical pairs. (Preprint).
O. Fujino, Effective base point free theorem for log canonical pairs--Kollár type theorem, Tohoku Math. J. (to appear).
O. Fujino, Effective base point free theorem for log canonical pairs II--Angehrn--Siu type theorems--, Michigan Math. J. (to appear).
O. Fujino, Theory of non-lc ideal sheaves--basic properties--. (Preprint).
O. Fujino, Introduction to the theory of quasi-log varieties. (Preprint).
O. Fujino, Finite generation of the log canonical ring in dimension four. (Preprint).
O. Fujino, Fundamental theorems for the log minimal model program. (Preprint).
J. Kollár and S. Mori, Birational geometry of algebraic varieties, Translated from the 1998 Japanese original, Cambridge Univ. Press, Cambridge, 1998.
