相关论文: Hypersurface exceptional singularities

We compute global log canonical thresholds of a large class of quasismooth well-formed del Pezzo weighted hypersurfaces in $\mathbb{P}(a_{1},a_{2},a_{3},a_{4})$. As a corollary we obtain the existence of orbifold K\"ahler--Einstein metrics…

We classify curvature homogeneous hypersurfaces in S^4 and H^4. In higher dimesnsion one only has the FKM examples and an isolate one by Tsukada of a hypersurface in H^5. Besides some simple examples, we show that there exists an isolated…

In this article, we prove that the commensurability class of a closed, orientable, hyperbolic 3-manifold is determined by the surface subgroups of its fundamental group. Moreover, we prove that there can be only finitely many closed,…

Non-Hermitian (NH) systems can display exceptional topological defects without Hermitian counterparts, exemplified by exceptional rings in NH two-dimensional systems. However, exceptional topological features associated with…

The authors study singular points of lightlike hypersurfaces of the de Sitter space S^{n+1}_1 and the geometry of hypersurfaces and use them for construction of an invariant normalization and an invariant affine connection of lightlike…

We construct complete normal forms for $5$-dimensional real hypersurfaces in $\mathbb C^3$ which are $2$-nondegenerate and also of Levi non-uniform rank zero at the origin point ${\bf p} =0$. The latter condition means that the rank of the…

A singularity is said to be exceptional (in the sense of V. Shokurov), if for any log canonical boundary, there is at most one exceptional divisor of discrepancy -1. In our previous paper (math.AG/9805004) we found two examples of…

In this paper, we study the algebraic hyperbolicity of very general surfaces in general Fano threefolds with Picard number one. We completely classify the algebraically hyperbolicity of those surfaces, except for surfaces in weighted…

In the authors' previous work, it was shown that if a zero mean curvature $C^4$-differentiable hypersurface in an arbitrarily given Lorentzian manifold admits a degenerate light-like point, then the hypersurface contains a light-like…

We show that if a homogeneous polynomial $f$ in $n$ variables has Waring rank $n+1$, then the corresponding projective hypersurface $f=0$ has at most isolated singularities, and the type of these singularities is completely determined by…

This paper addresses the well-posedness of a general class of bulk-surface convective Cahn--Hilliard systems with singular potentials. For this model, we first prove the existence of a global-in-time weak solution by approximating the…

We study birational transformations into elliptic fibrations and birational automorphisms of quasismooth anticanonically embedded weighted Fano 3-fold hypersurfaces having terminal singularities classified by A.R. Iano-Fletcher, J. Johnson,…

We study CR hypersurfaces in $\mathbb{C}^4$ that are Levi degenerate with constant rank Levi form, and moreover finitely nondegenerate. Each of these can be described as a deformation of a model CR hypersurface by adding terms of higher…

We study local rigidity properties of holomorphic embeddings of real hypersurfaces in $\mathbb C^2$ into real hypersurfaces in $\mathbb C^3$ and show that infinitesimal conditions imply actual local rigidity in a number of (important)…

The purpose of this paper is to point out a relation between the canonical sheaf and the intersection complex of a singular algebraic variety. We focus on the hypersurface case. Let $M$ be a complex manifold, $X\subset M$ a singular…

Let $X^n$ be a nonsingular hypersurface of degree $d\geq 2$ in the projective space $\mathbb{P}^{n+1}$ defined over a finite field $\mathbb{F}_q$ of $q$ elements. We prove a Homma-Kim conjecture on a upper bound about the number of…

In this paper, we prove that the Milnor fibre of a singularity over an i.c.i.s. of dimension 3 has the homotopy type of a bouquet of spheres, provided that the function that defines the singularity has finite extended codimension with…

Exceptional points in non-Hermitian systems have recently been shown to possess nontrivial topological properties, and to give rise to many exotic physical phenomena. However, most studies thus far have focused on isolated exceptional…

In this series of lectures, I will discuss results for complex hypersurfaces with non-isolated singularities. In Lecture 1, I will review basic definitions and results on complex hypersurfaces, and then present classical material on the…

We say that a subset of $\mathbb{P}^n(\mathbb{R})$ is maximally singular if its contains points with $\mathbb{Q}$-linearly independent homogenous coordinates whose uniform exponent of simultaneous rational approximation is equal to $1$, the…