Related papers: Singularities in positive characteristic, stratifi…
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 review properties of closed meromorphic $1$-forms and of the foliations defined by them. We present and explain classical results from foliation theory, like index theorems, the existence of separatrices, and resolution of singularities…
We study holomorphic vector fields whose singular locus contains a local complete intersection smooth positive-dimensional component. We prove global and local formulas expressing the limiting Milnor/Poincare-Hopf contribution along such a…
We give a new differential proof of our result on the maximal rank of generic unions of points of multiplicity two in projective space in degrees greater than five. This simplifies somewhat our proof of the Waring conjecture.
We propose to extend ``invertibility'' to ``regularity'' for categories in general abstract algebraic manner. Higher regularity conditions and ``semicommutative'' diagrams are introduced. Distinction between commutative and…
In dimensions greater than or equal to 3, the local structure of a singular holomorphic foliation conceals a globally defined foliation on the projective space of dimension one less. In this paper, we will discuss how the global dynamics of…
We introduce braid monodromy for the discriminant hypersurface in versal unfoldings of hypersurface singularities. Our objective is then to compute this invariant for singularities of Brieskorn Pham type: First we consider the unfolding by…
The singularities of the electromagnetic field are derived to include all the point-like multipoles representing an electric charge and current distribution. We show that for higher orders, it is more efficient to have fields represented in…
Blowing up a rational surface singularity in a reflexive module gives a (any) partial resolution dominated by the minimal resolution. The main theorem shows how deformations of the pair (singularity, module) relates to deformations of the…
In this paper we extend the notion of Futaki invariant to big and nef classes in such a way that it defines a continuous function on the \K\ cone up to the boundary. We apply this concept to prove that reduced normal crossing singularities…
Given a monoidal $\infty$-category $C$ equipped with a monoidal recollement, we give a simple criterion for an object in $C$ to be dualizable in terms of the dualizability of each of its factors and a projection formula relating them.…
We give a general method of constructing positive stable model structures for symmetric spectra over an abstract simplicial symmetric monoidal model category. The method is based on systematic localization, in Hirschhorn's sense, of a…
Simplicial arrangements are classical objects in discrete geometry. Their classification remains an open problem but there is a list conjectured to be complete at least for rank three. A further important class in the theory of hyperplane…
We construct Morse homology groups associated with any regular function on a smooth complex algebraic variety, allowing singular and non-compact critical loci. These groups are generated by critical points of a certain large pertubation of…
A variant of Siu's analyticity theorem is proved for relative types of plurisubharmonic functions. Some results on propagation of plurisubharmonic singularities and maximality of pluricomplex Green functions with analytic singularities are…
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…
Singularities of even smooth functions are studied. A classification of singular points which appear in typical parametric families of even functions with at most five parameters is given. Bifurcations of singular points near a caustic…
We introduce higher $F$-rationality generalising $F$-rationality. We prove that a normal variety over a field of characteristic zero is $m$-rational if and only if it is $m$-$F$-rational after reduction modulo a sufficiently large prime…
Using a part of XJC-correspondence by Pirio and Russo, we classify cubic forms $f$ whose Hessian matrices induce matrix factorizations of themselves. When it defines a reduced hypersurface, it satisfies the "secant-singularity"…
In view of the well-known correspondence between gravitational fields and space-time distributions on a world manifold X, the criterion of gravitation singularities as singularities of these distributions is suggested. In the germ terms,…