Related papers: Simple Cohen-Macaulay Codimension 2 Singularities

In this paper we obtain an explicit formula for the number of curves in two dimensional complex projective space, of degree d, passing through d(d+3)/2-(k+1) generic points and having one node and one codimension k singularity, where k is…

Generalizing an old result proved by P. Rao [see MR 83i:14025] for arithmetically Cohen-Macaulay, self-linked subschemes of codimension 2 in the projective n-space P, we give a characterization of self-linked pure subschemes of codimension…

We prove that a Cohen-Macaulay normal variety $X$ has Du Bois singularities if and only if $\pi_*\omega_{X'}(G) \simeq \omega_X$ for a log resolution $\pi: X' \to X$, where $G$ is the reduced exceptional divisor of $\pi$. Many basic…

In this paper we focus on various aspects of singular complex plane curves, mostly in the context of their homological properties and the associated combinatorial structures. We formulate some challenging open problems that can point to new…

We study the degeneration problem for maximal Cohen-Macaulay modules and give several examples of such degenerations. It is proved that such degenerations over an even-dimensional simple hypersurface singularity of type $(A_n)$ are given by…

We study Levi-flat real analytic hypersurfaces with singularities. We prove that the Levi foliation on the regular part of the hypersurface can be holomorphically extended, in a suitable sense, to neighbourhoods of singular points.

We consider globally hyperbolic spacetimes with compact Cauchy surfaces in a setting compatible with the presence of a positive cosmological constant. More specifically, for 3+1 dimensional spacetimes which satisfy the null energy condition…

In analogy to what happens in finite dimensions we state the Normal Form Theorem for k-singularities, introduced in the previous paper of the series. By means of that we study the local behaviour near a singularity i.e. we deduce local…

Some aspects of the multidimensional soliton geometry are considered. It is shown that some simples (2+1)-dimensional equations are exact reductions of the Self-Dual Yang-Mills equation or its higher hierarchy.

This is a part survey part research paper studying the local topology of complex analytic spaces. We review and strengthen the results of Kapovich--Koll\'ar "Fundamental groups of links of isolated singularities" (1109.4047) and incorporate…

We conduct a systematic search of codimension 2 Complete Intersection Calabi--Yau threefolds (CICY3) in rank 2 toric ambient spaces and fibered by complete intersection of a quadric and a cubic in $\C\P^4$. We classify both the nonsingular…

In this article we prove that for a large class of 2-dimensional minimal cones (including almost all 2-dimensional minimal cones that we know), the almost orthogonal union of any two of them is still a minimal cone. Comparing to existing…

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…

We enumerate the singular algebraic curves in a complete linear system on a smooth projective surface. The system must be suitably ample in a rather precise sense. The curves may have up to eight nodes, or a triple point of a given type and…

We show uniqueness up to sign of positive, orthogonal almost-Kaehler structures on any non-scalar flat Kaehler-Einstein surface.

We construct examples of flat surfaces in $\mathbb{H}^3$ which are graphs over a two-punctured horosphere and classify complete embedded flat surfaces in $\mathbb{H}^3$ with only one end and at most two isolated singularities.

For a weighted quasihomogeneous two dimensional hypersurface singularity, we define a smoothing with unipotent monodromy and an isolated graded normal singularity. We study the natural weighted blow up of both the smoothing and the surface.…

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…

We prove a reformulation of the multiplicity upper bound conjecture and use that reformulation to prove it for three-dimensional simplicial complexes and homology manifolds with many vertices. We provide necessary conditions for a…

In this paper we give a characterization of the possible homology groups that can occur for compact simply connected cohomogeneity one manifolds in dimensions seven and lower.