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ON THE PROJECTIVE FOURFOLDS WITH ALMOST NUMERICALLY POSITIVE CANONICAL DIVISORS
Fukuda, Shigetaka Korean Mathematical Society 2006 대한수학회보 Vol.43 No.4
Let X be a four-dimensional projective variety defined over the field of complex numbers with only terminal singularities. We prove that if the intersection number of the canonical divisor K with every very general curve is positive (K is almost numerically positive) then every very general proper subvariety of X is of general type in ';he viewpoint of geometric Kodaira dimension. We note that the converse does not hold for simple abelian varieties.
The Harbourne-Hirschowitz condition and the anticanonical orthogonal property for surfaces
Abel Castorena,Juan Bosco Frias-Medina 대한수학회 2023 대한수학회지 Vol.60 No.2
In this paper we give the first steps toward the study of the Harbourne-Hirschowitz condition and the anticanonical orthogonal property for regular surfaces. To do so, we consider the Kodaira dimension of the surfaces and study the cases based on the Enriques-Kodaira classification.