Related papers: Characteristic Classes of Hypersurfaces and Charac…

We show that there exist flat surface bundles with closed leaves having non-trivial normal bundles. This leads us to compute the Abelianisation of surface diffeomorphism groups with marked points. We also extend a formula of Tsuboi that…

This paper is about one dimensional families of cyclic covers of the projective line in positive characteristic. For each such family, we study the mass formula for the number of non-ordinary curves in the family. We prove two equations for…

In this work, we provide a local classification of certain special classes of surfaces determined by the prescription of the radial mean curvature in terms of the height and angle functions. Moreover, we introduce a special class of…

Let $X$ be a nonsingular variety defined over an algebraically closed field of characteristic $0$, and $D$ be a free divisor with Jacobian ideal of linear type. We compute the Chern class of the sheaf of logarithmic derivations along $D$…

We extend Wolff's "local smoothing" inequality to a wider class of not necessarily conical hypersurfaces of codimension 1. This class includes surfaces with nonvanishing curvature, as well as certain surfaces with more than one flat…

In this paper we construct a large class of new normal forms for Levi-nondegenerate real hypersurfaces in complex spaces. We adopt a general approach illustrating why these normal forms are natural and which role is played by the celebrated…

We study the geometry and topology of Hilbert schemes of points on the orbifold surface [C^2/G], respectively the singular quotient surface C^2/G, where G is a finite subgroup of SL(2,C) of type A or D. We give a decomposition of the…

We study hypersurfaces with fractional mean curvature in N-dimensional Euclidean space. These hypersurfaces are critical points of the fractional perimeter under a volume constraint. We use local inversion arguments to prove existence of…

We obtain a formula for the generating series of (the push-forward under the Hilbert-Chow morphism of) the Hirzebruch homology characteristic classes of the Hilbert schemes of points for a smooth quasi-projective variety of arbitrary pure…

We define a renormalized characteristic class for Einstein asymptotically complex hyperbolic (ACHE) manifolds of dimension 4: for any such manifold, the polynomial in the curvature associated to the characteristic class euler-3signature is…

In this paper, we give some new characterizations of umbilic hypersurfaces in general warped product manifolds, which can be viewed as generalizations of the work in \cite{KLP18} and \cite{WX14}. Firstly, we prove the rigidity for…

We introduce a notion of `proChow group' of varieties, agreeing with the notion of Chow group for complete varieties and covariantly functorial with respect to arbitrary morphisms. We construct a natural transformation from the functor of…

The (homogeneous) Essentially Isolated Determinantal Variety is the natural generalization of generic determinantal variety, and is fundamental example to study non-isolated singularities. In this paper we study the characteristic classes…

There are several ways to generalize characteristic classes for singular algebraic varieties. The simplest ones to describe are Chern-Mather classes obtained by Nash blow up. They serve as an ingredient to construct…

We consider the problem of computing the Euler characteristic of an abstract simplicial complex given by its vertices and facets. We show that this problem is #P-complete and present two new practical algorithms for computing Euler…

Thurston obtained a classification of individual surface homeomorphisms via the dynamics of the corresponding mapping class elements on Teichm\"uller space. In this paper we present certain extended versions of this, first, to random…

A multidimensional generalization of the Bernstein class of functions and the properties of functions of the introduced class are examined. In particular, a new proof of the integral representation of Bernstein functions of many variables…

Many eigenvalue matrix models possess a peculiar basis of observables which have explicitly calculable averages. This explicit calculability is a stronger feature than ordinary integrability, just like the cases of quadratic and Coulomb…

We establish a generic vanishing theorem for surfaces in characteristic $p$ that lift to $W_2(k)$ and use it for surface classification of surfaces of general type with Euler characteristic 1 and large Albanese dimension.

We introduce a method for studying reduction types of arithmetic curves and wildly ramified base change. We give new proofs of earlier results of Lorenzini and Obus-Wewers, and resolve a question of Lorenzini on the Euler characteristic of…