Related papers: Classification of threefold enc cDV quotient singu…

A complete classification of finitely generated involutive commutative two-valued groups is obtained. Three series of such two-valued groups are constructed: principal, unipotent and special, and it is shown that any finitely generated…

We evaluate one-dimensional representations of quantum symmetric conjugacy classes of classical matrix groups along with their quantum stabilizer subgroups.

We investigate equivariant birational geometry of rational surfaces and threefolds from the perspective of derived categories.

We complete the classification of hyperelliptic threefolds, describing in an elementary way the hyperelliptic threefolds with group $D_4$. These are algebraic and form an irreducible 2-dimensional family. Our paper is fully self-contained.

We develop an exact analytical approach to the optical response of a quantum dot-microcavity system for arbitrary excitation strengths. The response is determined in terms of the complex amplitudes of transitions between the rungs of the…

We introduce K3 transitions as a geometric approach to studying canonical 3-folds. These transitions link different deformation classes of canonical 3-folds via a combination of birational contractions and smoothings. As applications, we…

In order to find useful information to complete the classification of Enriques-Fano threefolds, we will computationally study the singularities of some known Enriques-Fano threefolds of genus 6, 7, 8, 9, 10, 13 and 17. We will also deduce…

We study the geometry of quintic threefolds $X\subset \mathbb{P}^4$ with only ordinary triple points as singularities. In particular, we show that if a quintic threefold $X$ has a reducible hyperplane section then $X$ has at most $10$…

In this paper, We introduce an invariant of rational n-tangles which is obtained from the Kauffman bracket. It forms a vector with Laurent polynomial entries. We prove that the invariant classifies the rational 2-tangles and the reduced…

We give a classification of Jordan-Chevalley decompositions of an endomorphism of a finite-dimensional vector space over a not necessarily perfect field, i.e. additive decompositions into commuting semisimple and nilpotent endomorphisms.

Let $X$ be a smooth projective rationally connected threefold with nef anticanonical divisor. We give a classification for the case when $-K_X$ is not semi-ample.

We provide a complete classification of the singularities of cluster algebras of finite cluster type. This extends our previous work about the case of trivial coefficients. Additionally, we classify the singularities of cluster algebras for…

In this paper, we classify irregular threefolds with numerically trivial canonical divisors in positive characteristic. For such a variety, if its Albanese dimension is not maximal, then the Albanese morphism will induce a fibration which…

We define the notion of complex stratification by quasifolds and show that such spaces occur as complex quotients by certain nonclosed subgroups of tori associated to convex polytopes. The spaces thus obtained provide a natural…

Any ample Cartier divisor D on a projective variety X is strictly nef (i.e. D.C>0 for any effective curve C on X). In general, the converse statement does not hold. But this is conjectured to be true for anticanonical divisors. The present…

Ternary real-valued quartics in $\mathbb{R}^3$ being invariant under octahedral symmetry are considered. The geometric classification of these surfaces is given. A new type of surfaces emerge from this classification.

Non-classical virtual knots may have non-isomorphic upper and lower quandles. We exploit this property to define the quandle difference invariant, which can detect non-classicality by comparing the numbers of homomorphisms into a finite…

We define and discuss an extension of the SpinC quantization concept to odd-dimensional manifolds. After that we describe its relation to (the usual) even-dimensional SpinC quantization and how its famous properties like "Quantization…

In this report, we propose a quick survey of the currently known techniques for encoding a Boolean cardinality constraint into a CNF formula, and we discuss about the relevance of these encodings. We also propose models to facilitate…

The defect of a cubic threefold $X$ with isolated singularities is a global invariant that measures the failure of $\mathbb{Q}$-factoriality. We compute the defect for such cubics in terms of topological data about the curve of lines…