Related papers: An application of the canonical bundle formula

In this article we study modules over wild canonical algebras which correspond to extension bundles [9] over weighted projective lines. We prove that all modules attached to extension bundles can be established by matrices with coefficients…

Canonical bundle formula due to Kawamata and others has played fundamental roles in algebraic geometry. We show that the canonical bundle formula has analytic characterization in terms of fiberwise integration, which confirms a folklore…

In this article we prove analogs of Kawamata's canonical bundle formula, Kawamata subadjunction and plt/lc inversion of adjunction for generalized pairs on Kaehler varieties. We also show that a conjecture of BDPPin dimension n-1 implies…

We prove the Bloch conjecture : $ c_2(E) \in H^4_\cald (X,\bbz(2))$ is torsion for holomorphic rank two vector bundles $E$ with an integrable connection over a complex projective variety $X$. We prove also the rationality of the…

Using our earlier results on polynomiality properties of plethystic logarithms of generating series of certain type we show that Schiffmann's formulas for various counts of Higgs bundles over finite fields can be reduced to much simpler…

Given any irreducible smooth complex projective curve $X$, of genus at least $2$, consider the moduli stack of vector bundles on $X$ of fixed rank and determinant. It is proved that the isomorphism class of the stack uniquely determines the…

We show that the moduli space of rank three toric vector bundles on smooth projective toric varieties satisfies Murphy's law, that is, every singularity type of finite type arises somewhere on this space.

The main purpose of this notes is to supplement the paper reid, which treated Minimal Model Program (also called Mori's Program) on toric varieties. We calculate lengths of negative extremal rays of toric varieties. As an application, we…

We prove a theorem of Hinich type on existence of a model structure on a category related by an adjunction to the category of differential graded modules over a graded commutative ring.

Using the notion of a valuation into the semifield of piecewise linear functions, we give a classification of torus equivariant flat families of finite type over a toric variety base, by certain piecewise linear maps between fans. As a…

We present an algorithm for computing line bundle valued cohomology classes over toric varieties. This is the basic starting point for computing massless modes in both heterotic and Type IIB/F-theory compactifications, where the manifolds…

We prove that the $\ell$-adic Chern classes of canonical extensions of automorphic vector bundles, over toroidal compactifications of Shimura varieties of Hodge type over $\bar{ \mathbb{Q}}_p$, descend to classes in the $\ell$-adic…

We prove that the non-vanishing conjecture and the log minimal model conjecture for projective log canonical pairs can be reduced to the non-vanishing conjecture for smooth projective varieties such that the boundary divisor is zero.

We generalize the Tian-Todorov Theorem in the case of Calabi-Yau varieties equipped with a line bundle.

We prove a formula for the motive of the stack of vector bundles of fixed rank and degree over a smooth projective curve in Voevodsky's triangulated category of mixed motives with rational coefficients.

We characterize Lelong classes on a toric manifold with an ample torus invariant line bundle, generalizing an approximation theorem due to Siciak. We include a counterexample to the theorem when the line bundle is globally generated, but…

The purpose of this paper is to prove the localization theorem for torus actions in equivariant intersection theory. Using the theorem we give another proof of the Bott residue formula for Chern numbers of bundles on smooth complete…

This is an expository article on the recent developments of Hodge theory on moduli spaces of smooth projective varieties with semi-ample canonical line bundles.

In these notes a recently developed technique for the computation of line bundle-valued sheaf cohomology group dimensions on toric varieties is reviewed. The key result is a vanishing theorem for the contributing components which depends on…

We consider the union of certain irreducible components of cohomological support loci of the canonical bundle, which we call standard. We prove a structure theorem about them and single out some particular cases, recovering and improving…