ﻻ يوجد ملخص باللغة العربية
We prove that the product of an Enriques surface and a very general curve of genus at least 1 does not satisfy the integral Hodge conjecture for 1-cycles. This provides the first examples of smooth projective complex threefolds of Kodaira dimension zero for which the integral Hodge conjecture fails, and the first examples of non-algebraic torsion cohomology classes of degree 4 on smooth projective complex threefolds.
In this note, we apply the semi-ampleness criterion in Lemma 3.1 to prove many classical results in the study of abundance conjecture. As a corollary, we prove abundance for large Kodaira dimension depending only on [BCHM10].
The Hodge conjecture is a major open problem in complex algebraic geometry. In this survey, we discuss the main cases where the conjecture is known, and also explain an approach by Griffiths-Green to solve the problem.
John Lesieutre constructed an example satisfying $kappa_sigma e kappa_ u$. This says that the proof of the inequalities in Theorems 1.3, 1.9, and Remark 3.8 in [O. Fujino, On subadditivity of the logarithmic Kodaira dimension, J. Math. Soc. Japan 69
In this paper we will prove a uniformity result for the Iitaka fibration $f:X rightarrow Y$, provided that the generic fiber has a good minimal model and the variation of $f$ is zero or that $kappa(X)=rm{dim}(X)-1$.
We review a combinatoric approach to the Hodge Conjecture for Fermat Varieties and announce new cases where the conjecture is true.