Nef anti-canonical divisors and rationally connected fibrations
Sho Ejiri, Yoshinori Gongyo
TL;DR
This paper investigates the properties of nef anti-canonical divisors on complex projective varieties with klt singularities, establishing a link between the Iitaka-Kodaira dimension and the dimensions of rationally connected fibrations.
Contribution
It proves a new inequality relating the Iitaka-Kodaira dimension of nef anti-canonical divisors to the dimensions of fibers in the maximal rationally connected fibration.
Findings
Dimension of general fiber ≥ Iitaka-Kodaira dimension of the anti-canonical divisor
Nef anti-canonical divisors influence the structure of rationally connected fibrations
New results on the Iitaka-Kodaira dimension for varieties with klt singularities
Abstract
We study the Iitaka-Kodaira dimension of nef relative anti-canonical divisors. As a consequence, we prove that given a complex projective variety with klt singularities, if the anti-canonical divisor is nef, then the dimension of a general fibre of the maximal rationally connected fibration is at least the Iitaka-Kodaira dimension of the anti-canonical divisor.
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