Related papers: Complements to ample divisors and Singularities
In this paper we describe the algebra of differential invariants for GL(n,C)-structures. This leads to classification of almost complex structures of general positions. The invariants are applied to the existence problem of…
K\"ahler's paper "\"Uber die Verzweigung einer algebraischen Funktion zweier Ver\"anderlichen in der Umgebung einer singul\"aren Stelle" offered a more perceptual view of the link of a complex plane curve singularity than that provided…
We investigate geometric properties of surfaces given by certain formulae. In particular, we calculate the singular curvature and the limiting normal curvature of such surfaces along the set of singular points consisting of singular points…
Let $X$ be a projective manifold of dimension $n$. Suppose that $T_X$ contains an ample subsheaf. We show that $X$ is isomorphic to $\mathbb{P}^n$. As an application, we derive the classification of projective manifolds containing a…
For any arbitrary algebraic curve, we define an infinite sequence of invariants. We study their properties, in particular their variation under a variation of the curve, and their modular properties. We also study their limits when the…
A continuous cohomology theory for topological quandles is introduced, and compared to the algebraic theories. Extensions of topological quandles are studied with respect to continuous 2-cocycles, and used to show the differences in second…
We study the topology of complements of caustics of function singularities of low codimensions, in particular 1) complete the enumeration of connected components of the complements of caustics of {\em simple} (in the sense of V.Arnold)…
We study torsion properties of the twisted Alexander modules of the affine complement $M$ of a complex essential hyperplane arrangement, as well as those of punctured stratified tubular neighborhoods of complex essential hyperplane…
We study singularities obtained by the contraction of the maximal divisor in compact (non kaehlerian) surfaces which contain global spherical shells. These singularities are of genus 1 or 2, may be Q-Gorenstein, numerically Gorenstein or…
We have proved that homeomorphisms of domains of Euclidean space, inverse of which distort the modulus of families of curves by Poletskii type, have a continuous extension to isolated boundary point.
We introduce new invariants of the projective plane (and, more generally, of certain toric surfaces) that arise from the appropriate enumeration of real elliptic curves. These invariants admit a refinement (according to the quantum index)…
During the years 1940-1970, Alexandrov and the "Leningrad School" have investigated the geometry of singular surfaces in depth. The theory developed by this school is about topological surfaces with an intrinsic metric for which we can…
In recent times a great amount of progress has been achieved in symplectic and contact geometry, leading to the development of powerful invariants of 3-manifolds such as Heegaard Floer homology and embedded contact homology. These…
We show how quiver representations and their invariant theory natu- rally arise in the study of some moduli spaces parametrizing bundles dened on an algebraic curve, and how they lead to ne results regarding the geometry of these spaces.
The Arnold inequalities characterizing the topology of non-singular plane real algebraic curves and the generalization of these inequalities for nodal curves by Viro are extended in this paper for the curves whose singularities have…
In this paper we discuss an extension of Perelman's comparison for quadrangles. Among applications of this new comparison theorem, we study the equidistance evolution of hypersurfaces in Alexandrov spaces with non-negative curvature. We…
We explain how to derive largeness constraints in scalar curvature geometry using some basic splitting results and the potential theory on singular area minimizing hypersurfaces. This includes a variety of results like the non-existence of…
The main result of the present paper is a construction of relative moduli spaces of stable sheaves over the stack of quasipolarized projective surfaces. For this, we use the theory of good moduli spaces, whose study was initiated by Alper.…
We built the pluripotential theory on almost complex surfaces. Using Bedford-Taylor type relative capacities we prove among others that J-holomorphic curves as well as negligible sets are pluripolar and Josefson's type theorem on almost…
We build two embedded resolution procedures of a quasi-ordinary singularity of complex analytic hypersurface, by using toric morphisms which depend only on the characteristic monomials associated to a quasi-ordinary projection of the…