Related papers: Sur la laminarite de certains courants

A lamination $\lambda$ is $\epsilon$-thick (with respect to a basepoint $X$), if the Teichm\"uller ray from $X$ in the direction of $\lambda$ stays in the $\epsilon$-thick part. We show that, for surfaces of high enough genus, any two…

We prove uniform boundedness statements for semistable pure sheaves on projective manifolds. For example, we prove that the set of isomorphism classes of pure sheaves of dimension 2 that are slope semistable with respect to ample classes…

We show that every irreducible, simply connected curve on a toric affine surface X over the field of complex numbers is an orbit closure of a multiplicative group action on X. It follows that up to the action of the automorphism group…

Building on and extending tools from variational analysis, we prove Kuratowski convergence of sets of simplicial area minimizers to minimizers of the smooth Douglas-Plateau problem under simplicial refinement. This convergence is with…

We investigate the connection between Osserman limit series (on curves of pseudocompact type) and Amini-Baker limit linear series (on metrized complexes with corresponding underlying curve) via a notion of pre-limit linear series on curves…

Classification theory and the study of projective varieties which are covered by rational curves of minimal degrees naturally leads to the study of families of singular rational curves. Since families of arbitrarily singular curves are hard…

We study discrete curvatures computed from nets of curvature lines on a given smooth surface, and prove their uniform convergence to smooth principal curvatures. We provide explicit error bounds, with constants depending only on properties…

In this work we describe a class of subsets of the Euclidean plane which, with the induced length metric, are locally $CAT(0)$ spaces and we show that the gluing of two such subsets along a piece of their boundary is again a locally…

This article introduces and studies the tight approximation property, a property of algebraic varieties defined over the function field of a complex or real curve that refines the weak approximation property (and the known cohomological…

The purpose of this paper is to interpret the phase transition in the Loewner theory as an analog of the hyperbolic variant of the Schur theorem about curves of bounded curvature. We define a family of curves that have a certain conformal…

We propose a study of the foliations of the projective plane induced by simple derivations of the polynomial ring in two indeterminates over the complex field. These correspond to foliations which have no invariant algebraic curve nor…

Given a complex structure, we investigate diverging sequences of projective structures on the fixed complex structure in terms of Thurston's parametrization. In particular, we will give a geometric proof to the theorem by Kapovich stating…

We clearly refine the fundamental framework of the thin-layer quantization procedure, and further develop the procedure by taking the proper terms of degree one in $q_3$ ($q_3$ denotes the curvilinear coordinate variable perpendicular to…

For each closed surface of genus $g\ge3$, we find a finite subcomplex of the separating curve complex that is rigid with respect to incidence-preserving maps.

We develop recursive formulas for the horizontal and vertical monodromies of a quasi-ordinary surface. These are monodromies associated to the Milnor fiber of a slice transverse to a component of the singular locus. In the course of working…

In this paper we give an asymptotic bound of the cardinality of Zariski multiples of particular plane singular curves. These curves have only nodes and cusps as singularities and are obtained as branched curves of ramified covering of the…

We prove that the formal completion of a complex projective surface along a rigid smooth curve with trivial normal bundle determines the birational equivalence class of the surface.

We prove a result on the singularities of ball quotients $\Gamma\backslash\CC H^n$. More precisely, we show that a ball quotient has canonical singularities under certain restrictions on the dimension $n$ and the underlying lattice. We also…

We study the pull-back of regular 1-forms on a complex irreducible plane curve singularity under the normalization morphism.

We prove that the set of leaves of a holomorphic lamination of codimension one that are non-transversal to a germ of a holomorphic map is discrete.