Abstract
Letf:X→S be a projective morphism of noetherian schemes andL a line bundle onX. In this note we will give a condition for openness of the setS nef L ={∈S‖L s is nef onX s }.
Similar content being viewed by others
References
D. Gieseker, Stable vector bundles and the Frobenius morphism, Ann. Scient. Ec. Norm. Sup., 6 (1973), 95–101
M. Maruyama, Openness of a family of torsion free sheaves, J. Math. Kyoto Univ., 16 (1976), 627–637
Y. Miyaoka, The Chern Classes and Kodaira Dimension of a Minimal Variety, Advanced Studies in Pure Mathematics 10, 1987, Algebraic Geometry, Sendai, 1985, 449–476, Kinokuniya
A. Moriwaki, Semi-stably polarized fiber spaces and Bogomolov-Gieseker’s inequality, to appear in J. Math. Kyoto Univ.
Author information
Authors and Affiliations
Additional information
This article was processed by the author using the Springer-Verlag TEX mamath macro package 1990
Rights and permissions
About this article
Cite this article
Moriwaki, A. A criterion of openness of a family of nef line bundles. Manuscripta Math 75, 327–331 (1992). https://doi.org/10.1007/BF02567088
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02567088