Related papers: Five-Dimensional Weakly Exceptional Quotient Singu…
In this paper, we give a definition of weak stability condition on a triangulated category. The difference between our definition and existing definitions is that we allow objects in the kernel to have non-maximal phases. We then construct…
Optical singularities, which are positions within an electromagnetic field where certain field parameters become undefined, hold significant potential for applications in areas such as super-resolution microscopy, sensing, and…
A triangulation of a connected closed surface is called weakly regular if the action of its automorphism group on its vertices is transitive. A triangulation of a connected closed surface is called degree-regular if each of its vertices…
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…
As a generalization of a quasi-elliptic surface, there is a quasi-hyperelliptic surface, a nonsingular projective surface which has a fibration structure whose general fiber is a quasi-hyperelliptic curve ($=$ singular hyperelliptic curve…
Divisors with minimal discrepancy over cA points are classified
In this paper, we classify the configurations of the singular points which appear on the quotients of the projective plane by the $1$-foliations of degree $-1$ in characteristic $2$.
We give a potential alternative definition of a weak infinite dimensional category, in an unbiased fashion, using one one dimensional quiver with composition and extra structure.
A Q-homology plane is a normal complex algebraic surface having trivial rational homology. We obtain a structure theorem for Q-homology planes with smooth locus of non-general type. We show that if a Q-homology plane contains a non-quotient…
Weak-strong uniqueness property in the class of finite energy weak solutions is established for two different compressible liquid crystal systems by the method of relative entropy. To overcome the difficulties caused by the molecular…
We show that a complex planar curve homeomorphic to the projective line has at most four singular points. If it has exactly four then it has degree five and is unique up to a projective equivalence.
We prove that an alternating e-form on a vector space over a quasi-algebraically closed field always has a singular (e-1)-dimensional subspace, provided that the dimension of the space is strictly greater than e. Here an (e-1)-dimensional…
Let R be an associative ring with possible extra structure. R is said to be weakly small if there are countably many 1-types over any finite subset of R. It is locally P if the algebraic closure of any finite subset of R has property P. It…
This paper concerns the formation of singularities in the classical $(5+1)$-dimensional, co-rotational Skyrme model. While it is well established that blowup is excluded in $(3+1)$-dimensions, nothing appears to be known in the higher…
For a normal subvariety $V$ of ${\bf C}^n$ with a good ${\bf C}^*$-action we give a simple characterization for when it has only log canonical, log terminal or rational singularities. Moreover we are able to give formulas for the…
The aim of this paper is twofold: First we classify all abstract light dual multinets of order $6$ which have a unique line of length at least two. Then we classify the weak projective embeddings of these objects in projective planes over…
In this paper the detailed classification of three-dimensional exceptional canonical hypersurface singularities which don't satisfy the condition of well-formedness is given. This result completes the classification of three-dimensional…
Weakly Schreier split extensions are a reasonably large, yet well-understood class of monoid extensions, which generalise some aspects of split extensions of groups. This short note provides a way to define and study similar classes of…
A weakly distance-regular digraph is quasi-thin if the maximum value of its intersection numbers is 2. In this paper, we focus on commutative quasi-thin weakly distance-regular digraphs, and classify such digraphs with valency more than 3.…
The most commonly encountered types of complex analytic G-structures and Cartan geometries cannot have singularities of complex codimension 2 or more.