Publisher : Department of Mathematics, Kyungpook National University
DOI : 10.5666/KMJ.2014.54.2.203
Title & Authors
Algebraic Fiber Space Whose Generic Fiber and Base Space Are of Almost General Type Fukuda, Shigetaka;
We assume that the existence and termination conjecture for flips holds. A complex projective manifold is said to be of almost general type if the intersection number of the canonical divisor with every very general curve is strictly positive. Let f be an algebraic fiber space from X to Y. Then the manifold X is of almost general type if every very general fiber F and the base space Y of f are of almost general type.
Of general type;Algebraic fiber space;
F. Ambro, Nef dimension of minimal models, Math. Ann., 330(2004), 309-322.
C. Birkar, P. Cascini, C. Hacon and J. McKernan, Existence of minimal models for varieties of log general type, J. Amer. Math. Soc., 23(2010), 405-468.
S. Fukuda, On the projective fourfolds with almost numerically positive canonical divisors, Bull. Korean Math. Soc., 43(2006), 763-770.
S. Fukuda, A note on the projective varieties of almost general type, Rocky Mountain J. Math., 40(2010), 501-512.
C. Hacon and J. McKernan, On the existence of flips, math. AG/0507597, July 2005.
Y. Kawamata, On the length of an extremal rational curve, Invent. Math., 105(1991), 609-611.
J. Kollar, Is there a topological Bogomolov-Miyaoka-Yau inequality?, Pure Appl. Math. Q., 4(2008), 203-236.
Y. Miyaoka and S. Mori, A numerical criterion for uniruledness, Ann. of Math., 124(1986), 65-69.
V. Shokurov, Prelimiting flips, Proc. Steklov Inst. Math., 240(2003), 75-213.
V. Viehweg, The additivity of the Kodaira dimension for projective fiber spaces over varieties of general type (German), J. Reine Angew. Math., 330(1982), 132-142.