Related papers: On semi-ampleness of the moduli part
In this short note we reduce the b-semiampleness conjecture for lc-trivial fibrations to the b-semiampleness conjecture for klt-trivial fibrations.
In this note, we prove effective semi-ampleness conjecture due to Prokhorov and Shokurov for a special case, more concretely, for Q-Gorenstein klt-trivial fibrations over smooth projective curves whose fibers are all klt log Calabi-Yau…
It has been conjectured by Prokhorov and Shokurov that the moduli part in the canonical bundle formula is effectively b-semiample. In this work we reduce this conjecture to the case where the base of the fibration has dimension one.…
The B-Semiampleness Conjecture of Prokhorov and Shokurov predicts that the moduli part in a canonical bundle formula is semiample on a birational modification. We prove that the restriction of the moduli part to any sufficiently high…
Fujino gave a proof in [Fuj03] for the semi-ampleness of the moduli part in the canonical bundle formula in the case when the general fibers are K3 surfaces or Abelian varieties. We show a similar statement when the general fibers are…
It is conjectured that the moduli b-divisor of the Kawamata-Kodaira canonical bundle formula associated to a klt-trivial fibration $(X,B)\to Z$ is semi-ample. In this paper, we show the semi-ampleness of an arbitrarily small perturbation of…
Let $f \colon (X,\Delta) \to Y$ be a fibration such that $K_X + \Delta$ is torsion along the fibres of $f$. Assume that $Y$ has dimension 2, or that $Y$ has dimension 3 and the fibres have dimension at most 3. Then the restriction of the…
We prove that if the moduli $\mathbb Q$-b-divisor of a basic slc-trivial fibration is b-numerically trivial then it is $\mathbb Q$-b-linearly trivial. As a consequence, we prove that the moduli part of a basic slc-trivial fibration is…
Roughly speaking, by using the semi-stable minimal model program, we prove that the moduli part of an lc-trivial fibration coincides with that of a klt-trivial fibration induced by adjunction after taking a suitable generically finite…
In this note, we reduce various conjectures in birational geometry, including Shokurov conjecture on singularities of the base of log Calabi-Yau fibrations of Fano type and boundedness conjecture for rationally connected Calabi-Yau…
In this paper, we investigate the moduli of surfaces of general type admitting genus 2 fibrations with irregularity q = g_b + 1, where g_b >= 2 is the genus of the base. We prove that smooth fibrations are parametrized by a unique component…
Generalizing the well-known Shafarevich hyperbolicity conjecture, it has been conjectured by Viehweg that a quasi-projective manifold that admits a generically finite morphism to the moduli stack of canonically polarized varieties is…
In this paper, we proved that, for a semi-stable fibration of a proper smooth surface to a proper smooth curve over a field of positive characteristic, if the generic fiber is ordinary, then the semi-positivity theorem holds. As an…
We revisit the notion of flatness for semimodules over semirings. In particular, we introduce and study a new notion of uniformly flat semimodules based on the exactness of the tensor functor. We also investigate the relations between this…
We investigate whether the group algebra of a finite group over a localisation of the integers is semiperfect. The main result is a necessary and sufficient arithmetic criterion in the ordinary case. In the modular case, we propose a…
In order to study the problems of extending an action along a quotient of the acted object and along a quotient of the acting object, we investigate some properties of the fibration of points. In fact, we obtain a characterization of…
We generalize some results of A.J. Sommese, B. Totaro and M.V. Brown, providing some geometric interpretations of the notion of partial ampleness.
Using the theory of moduli of curves, we establish various slope inequalities for general fibered surfaces. More precisely, we introduce the notion of functorial divisors on Artin stacks and prove a theorem concerning their effectiveness.…
We study semi--algebraic domains associated with symplectic tori and conjecturally identified with spaces of stability conditions on the Fukaya categories of these tori. Our motivation is to test which results from the theory of flat…
We describe a general setting for the definition of semi-infinite cohomology of finite dimensional algebras, and provide its categorical interpretation. We apply this interpretation to compute semi-infinite cohomology of some modules over…