Related papers: Characteristic Classes of Hypersurfaces and Charac…

Generalizing the star graphs of M\"uller-Stach and Westrich, we describe a class of graphs whose associated graph hypersurface is equipped with a non-trivial torus action. For such graphs, we show that the Euler characteristic of the…

In this article, we investigate some properties of cyclic coverings of complex surfaces of general type branched along smooth curves that are numerically equivalent to a multiple of the canonical class. The main results concern coverings of…

We study the category of matrix factorizations for an isolated hypersurface singularity. We compute the canonical bilinear form on the Hochschild homology of this category. We find explicit expressions for the Chern character and the…

We define a "circle Euler characteristic" of a circle action on a compact manifold or finite complex X. It lies in the first Hochschild homology group of ZG where G is the fundamental group of X. It is analogous in many ways to the ordinary…

An alternative, pedagogically simpler derivation of the allowed physical wave fronts of a propagating electromagnetic signal is presented using geometric algebra. Maxwell's equations can be expressed in a single multivector equation using…

In this paper we classify a kind of special Calabi hypersurfaces with negative constant sectional curvature in Calabi affine geometry. Meanwhile, we find a class of new Euclidean complete and Calabi complete affine hypersurfaces, which…

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…

In this paper, we prove some fundamental theorems for holomorphic curves on angular domain intersecting a hypersurface, finite set of fixed hyperplanes in general position and finite set of fixed hypersurfaces in general position on complex…

The goal of this work is to construct integral Chern classes and higher cycle classes for a smooth variety over a perfect field of characteristic p>0 that are compatible with the rigid Chern classes defined by Petrequin. The Chern classes…

The notions of (metric) hypersurface data were introduced in [Mars,2013] as a tool to analyze, from an abstract viewpoint, hypersurfaces of arbitrary signature in pseudo-riemannian manifolds. In this paper, general geometric properties of…

In this paper we introduce the Chern minimal surface in Hermitian surfaces by using the Chern connection, and we show that it only has isolated complex and anticomplex points for a generic one (neither holomorphic nor antiholomorphic). For…

In this paper we obtain some explicit expressions for the Euler characteristic of a rank n coherent sheaf F on P^N and of its twists F(t) as polynomials in the Chern classes c_i(F), also giving algorithms for the computation. The employed…

The main purpose of this article is to lay the foundations for a classification of isolated hypersurface singularities in positive characteristic. Although our article is in the spirit of Arnol'd who classified real an complex hypersurfaces…

Homology Hirzebruch characteristic classes for singular varieties have been recently defined by Brasselet-Schuermann-Yokura as an attempt to unify previously known characteristic class theories for singular spaces (e.g., MacPherson-Chern…

In this paper we give explicit formulas of differential characteristic classes of principal $G$-bundles with connections and prove their expected properties. In particular, we obtain explicit formulas for differential Chern classes,…

We give an overview of the fundamental definitions and results concerning hypersurface singularities, defined by convergent power series over an arbitrary real valued field. This approach combines, on the one hand, the classical case of…

What are called secondary characteristic classes in Chern-Weil theory are a refinement of ordinary characteristic classes of principal bundles from cohomology to differential cohomology. We consider the problem of refining the construction…

We offer a short proof of Connes' Hochschild class of the Chern character formula for non-unital semifinite spectral triples. The proof is simple due to its reliance on the authors' extensive work on a refined version of the local index…

We relate Fubini's theorem for Euler characteristics to Riemann-Hurwtiz formulae, and reprove a classical result of Iversen. The techniques used include algebraic geometry, complex geometry, and model theory. Possible applications to the…

A Hopf hypersurface in complex hyperbolic space CH^n is one in which the complex structure applied to the normal vector is a principal direction at each point. In this paper, Hopf hypersurfaces for which the corresponding principal…