Related papers: Lipschitz Stratification of Complex Hypersurfaces …

Let $\mathcal{H}$ be a Hurwitz space that parametrises holomorphic maps to $\mathbb{P}^1$. Abramovich, Corti and Vistoli, building on work of Harris and Mumford, describe a compactification $\overline{\mathcal{H}}$ with a natural boundary…

Let $f : X \to S$ be a smooth projective family defined over $\mathcal{O}_{K}[\mathcal{S}^{-1}]$, where $K \subset \mathbb{C}$ is a number field and $\mathcal{S}$ is a finite set of primes. For each prime $\mathfrak{p} \in…

In many cases involving mirror symmetry, it is important to have concrete mirror dual families. In this paper, we construct a natural crepant resolutions of the Batyrev-Borisov mirror dual family to the complete intersection of two cubic…

In this article, we consider an infinite family of normal surface singularities with an integral homology sphere link which is related to the family of space monomial curves with a plane semigroup. These monomial curves appear as the…

In this paper we show Whitney's fibering conjecture in the real and complex, local analytic and global algebraic cases. For a given germ of complex or real analytic set, we show the existence of a stratification satisfying a strong (real…

Using toric geometry, lattice theory, and elliptic surface techniques, we compute the Picard Lattice of certain K3 surfaces. In particular, we examine the generic member of each of M. Reid's list of 95 families of Gorenstein K3 surfaces…

Let X be an irreducible hypersurface in $\mathbb{P}^n$ of degree $d\geq 3$ with only isolated semi-weighted homogeneous singularities, such that $exp(\frac{2\pi i}{k})$ is a zero of the Alexander polynomial. Then we show that the…

We continue the development of the theory of infinitesimal Lipschitz equivalence, showing the genericity of the condition for families of hypersurfaces with isolated singularities.

In this paper we explore conditions for a curve in a smooth projective surface to have a free product of cyclic groups as the fundamental group of its complement. It is known that if the surface is $\mathbb P^2$, then such curves must be of…

We construct biregular models of families of log Del Pezzo surfaces with rigid cyclic quotient singularities such that a general member in each family is wellformed and quasismooth. Each biregular model consists of infinite series of such…

This is an expanded version of our work [AN88], 1988, in Russian. We classify del Pezzo surfaces over C with log terminal singularities of index \le 2. By classification, we understand a description of the intersection graph of all…

We give finite presentations for the fundamental group of moduli stacks of smooth Weierstrass curves over complex projective space P^n which extend the classical result for elliptic curves to positive dimensional base. We thus get natural…

The purpose, mainly expository and speculative, of this paper---an outgrowth of a survey lecture at the September 1997 Obergurgl working week---is to indicate some (not all) of the efforts that have been made to interpret equisingularity,…

Minkowski space is the local model of 3 dimensionnal flat spacetimes. Recent progress in the description of globally hyperbolic flat spacetimes showed strong link between Lorentzian geometry and Teichm{\"u}ller space. We notice that…

We study the topological triviality of families of singular surfaces in ${\mathbb C}^3$ parametrized by $\mathcal A$-finitely determined map germs. We prove that the constancy of the Milnor number of the double point locus characterizes the…

We introduce the class of weakly log canonical singularities, a natural generalization of semi-log canonical singularities. Toric varieties (associated to toric face rings, possibly non-normal or reducible) which have weakly (semi-) log…

We study the existence of a Chow-theoretic decomposition of the diagonal of a smooth cubic hypersurface, or equivalently, the universal triviality of its ${\rm CH}_0$-group. We prove that for odd dimensional cubic hypersurfaces or for cubic…

Using the path lattice cohomology we provide a conceptual topological characterization of the geometric genus for certain complex normal surface singularities with rational homology sphere links, which is uniformly valid for all…

We show that the topological classification and the smooth classification are generically the same for certain families of plane curves in a semi-local case(the double local case). Especially we give the normal form of transversely jointed…

Utilizing previously established results concerning costratification in relative tensor-triangular geometry, we classify the colocalizing subcategories of the singularity category of a locally hypersurface ring and then we generalize this…