相关论文: Canonical forms of 3d cusp-fold singularities and …

By developing a suitable version of the circle method, we show that the space of degree $e$ rational curves on a smooth hypersurface of degree $d$ has only canonical singularities provided its dimension is sufficiently large with respect to…

This paper consists in discussing some issues on generic local classification of typical singularities of $2D$ piecewise smooth vector fields when the switching set is an algebraic variety. The main focus is to obtain classification results…

We classify combinations of isolated singularities that can occur on complex cubic threefolds generalizing analogous results for cubic surfaces due to Schl\"{a}fli and Bruce--Wall. In addition, we provide concise combinatorial description…

In two parts, we present a bigness criterion for the cotangent bundle of resolutions of orbifold surfaces of general type. As a corollary, we obtain the \textit{canonical model singularities} (CMS) criterion that can be applied to determine…

In this paper, we study polyhedral 3-manifolds with nonnegative curvature and integral monodromy, two conditions motivated by Thurston's work in arXiv:math/9801088. We classify the 32 isometry types of codimension 3 singularities in such…

An inductive approach to classifying toric Fano varieties is given. As an application of this technique, we present a classification of the toric Fano threefolds with at worst canonical singularities. Up to isomorphism, there are 674,688…

We classify the canonical threefold singularities that allow an effective two-torus action. This extends classification results of Mori on terminal threefold singularities and of Ishida and Iwashita on toric canonical threefold…

We compute some numerical invariants of the lines on hyperplane sections of a smooth cubic threefold over complex numbers. We also prove that for any smooth hypersurface $X\subset \mathbb P^{n+1}$ of degree $d$ over an algebraically closed…

We conjecture that every three dimensional canonical singularity defines a five dimensional N=1 SCFT. Flavor symmetry can be found from singularity structure: non-abelian flavor symmetry is read from the singularity type over one…

There are six orientable, compact, flat 3-manifolds that can occur as cusp cross-sections of hyperbolic 4-manifolds. This paper provides criteria for exactly when a given commensurability class of arithmetic hyperbolic 4-manifolds contains…

Canonical matrices of (a) bilinear and sesquilinear forms, (b) pairs of forms, in which every form is symmetric or skew-symmetric, and (c) pairs of Hermitian forms are given over finite fields of characteristic not 2 and over finite…

This paper describes the construction of a canonical compactification of the space of trajectories and of the unstable/stable sets of a generic gradient like vector field on a closed manifold as well as a canonical structure of a smooth…

We survey determinantal singularities, their deformations, and their topology. This class of singularities generalizes the well studied case of complete intersections in several different aspects, but exhibits a plethora of new phenomena…

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…

This short note is some obvious mathematical addendum to our papers on Wilson loops on polygon-like contours with circular edges \cite{Dorn:2020meb,Dorn:2020vzj}. Using the technique of osculating spheres and circles we identify the…

We classify three-dimensional Fano varieties with canonical Gorenstein singularities of degree bigger than 64.

We prove that finite area isolated singularities of surfaces with constant positive curvature in R^3 are removable singularities, branch points or immersed conical singularities. We describe the space of immersed conical singularities of…

We show that the singularities of spacelike maximal surfaces in Lorentz-Minkowski 3-space generically consist of cuspidal edges, swallowtails and cuspidal cross caps. The same result holds for spacelike mean curvature one surfaces in de…

We aim to classify codimension 1 foliations $\mathscr{F}$ with canonical singularities and $\nu(K_{\mathscr{F}}) < 3$ on threefolds of general type. We prove a classification result for foliations satisfying these conditions and having…

Canonical threefold singularities in M-theory and Type IIB string theory give rise to superconformal field theories (SCFTs) in 5d and 4d, respectively. In this paper, we study canonical hypersurface singularities whose resolutions contain…