相关论文: Log canonical models of foliated surfaces

We prove that the morphism that maps a rational ruled surface to its singular locus is genericaly injective modulo isomophism and duality. We also calculate the dimension and the degre of its image.

We prove that the moduli b-divisor of an lc-trivial fibration from a log canonical pair is log abundant. The result follows from a theorem on the restriction of the moduli b-divisor, based on a theory of lc-trivial morphisms, which allows…

Let $\Lambda$ be a finite dimensional algebra over an algebraically closed field. Criteria are given which characterize existence of a fine or coarse moduli space classifying, up to isomorphism, the representations of $\Lambda$ with fixed…

We show that every coarse moduli space, parametrizing complex special linear rank two local systems with fixed boundary traces on a surface with nonempty boundary, is log Calabi-Yau in that it has a normal projective compactification with…

Recent work ([18], [1]) has produced a complete list of weighted homogeneous surface singularities admitting smoothings whose Milnor fibre has only trivial rational homology (a "rational homology disk"). Though these special singularities…

We formulate a stable reduction conjecture that extends Deligne-Mumford's stable reduction to higher dimensions and provide a simple proof that it holds in large characteristic, assuming two standard conjectures of the Minimal Model…

In this paper the authors consider a certain toroidal compactification of the moduli space of degenerations of (1,p)-polarized abelian surfaces with (canonical) level structure. Using Hodge theory we give a proof that a degenerate abelian…

We show that if $(X_t,\mathcal{F}_t)_t$ is a family of foliations with reduced singularities on a smooth family of surfaces, then invariance of plurigenera holds for sufficiently large $m$. On the other hand, we provide examples on which…

We give a bound on which singularities may appear on Koll\'ar--Shepherd-Barron--Alexeev stable surfaces for a wide range of topological invariants and use this result to describe all stable numerical quintic surfaces (KSBA-stable surfaces…

We provide several applications of the minimal model program to the local and global study of co-rank one foliations on threefolds. Locally, we prove a singular variant of Malgrange's theorem, a classification of terminal foliation…

We prove the existence of log canonical modifications for a log pair. As an application, together with Koll\"ar's gluing theory, we remove the assumption in the first named author's work [Odaka11], which shows that K-semistable polarized…

We prove existence of flips, special termination, the base point free theorem and, in the case of log general type, the existence of minimal models for F-dlt foliated pairs of co-rank one on a $\mathbb Q$-factorial projective threefold. As…

We prove that, under mild restrictions, the space of codimension-one foliations of degree one on a smooth projective complete intersection has two irreducible components of logarithmic type. We also prove that the same conclusion holds for…

The nonvanishing conjecture for projective log canonical pairs plays a key role in the minimal model program of higher dimensional algebraic geometry. The numerical nonvanishing conjecture considered in this paper is a weaker version of the…

We show that mixed-characteristic and equi-characteristic small deformations of 3-dimensional canonical (resp. terminal) singularities with perfect residue field of characteristic $p>5$ are canonical (resp. terminal). We discuss…

We prove the normality of minimal log canonical centers on threefold pairs which residue fields are perfect of residue characteristics $p\neq 2,3 $ and $5$. We also show that the union of all log canonical centers on threefold pairs with…

In this article we present a formula for the plurigenera of minimal models of nondegenerate toric hypersurfaces, which is valid in arbitrary dimension and which expresses these invariants through lattice points on the Fine interior. From…

In this paper we give simple proofs for the bounds (some of them sharp) of the difference of the moduli of the second and the first logarithmic coefficient for the general class of univalent functions and for the class of convex univalent…

We study holomorphic foliations on normal crossings varieties arising as semistable degenerations. We do so by we exploring the notion of foliated d-semistability using the language of logarithmic structures in the sense of…

We study and classify linearly normal surfaces in $\mathbf{P}^n$, of degree $d$ and sectional genus $g$, such that $d\geq 2g-1$.