Related papers: Classification of sextics of torus type

In the present article, we investigate the topology of real toric varieties, especially those whose torus is not split over the field of real numbers. We describe some canonical fibrations associated to their real loci. Then, we establish…

We provide new forbidden criterion for realizability of smooth tropical plane curves. This in turn provides us a complete classification of smooth tropical plane curves up to genus six.

In this paper we obtain the complete classification of the inequivalent classes of M2-brane symplectic torus bundles with monodromy in $SL(2,Z)$ and their precise U-duality relations among them. There are eight inequivalent classes of…

We identify a link between regular matroids and torus representations all of whose isotropy groups have an odd number of components. Applying Seymour's 1980 classification of the former objects, we obtain a classification of the latter. In…

We give a simplified definition of topological T-duality that applies to arbitrary torus bundles. The new definition does not involve Chern classes or spectral sequences, only gerbes and morphisms between them. All the familiar topological…

The finiteness problem of stationary configurations for the planar five-vortex problem is considered in this paper. The numbers of equilibria and rigidly translating configurations are shown to be at most 6 and 24 respectively. The numbers…

In the classification of real singularities by Arnold et al. (1985), normal forms, as representatives of equivalence classes under right equivalence, are not always uniquely determined. We describe the complete structure of the equivalence…

The moduli space of flat SL(2,R)-connections modulo gauge transformations on the torus may be described by ordered pairs of commuting SL(2,R) matrices modulo simultaneous conjugation by SL(2,R) matrices. Their spectral properties allow a…

Let X be a smooth projective curve of genus at least two over the complex numbers. A pair (E,\phi) over X consists of an algebraic vector bundle E over X and a holomorphic section \phi of E. There is a concept of stability for pairs which…

We systematically study how the integrality of the conformal characters shapes the space of fermionic rational conformal field theories in two dimensions. The integrality suggests that conformal characters on torus with a given choice of…

The parameters 2-(36,15,6) are the smallest parameters of symmetric designs for which a complete classification up to isomorphism is yet unknown. Bouyukliev, Fack and Winne classified all 2-$(36,15,6)$ designs that admit an automorphism of…

We first formulate a general scheme for the classification of 2-compact groups in terms of maximal torus normalizer pairs. Applying this scheme, we show that all connected and some non-connected 2-compact groups are N-determined. We also…

We describe all possible topological structures of Morse flows and typical gradient saddle-nod bifurcation of flows on the 2-dimensional torus with a hole in the case that the number of singular point of flows is at most six. To describe…

We provide a complete classification of six-dimensional symmetric toroidal orbifolds which yield N>=1 supersymmetry in 4D for the heterotic string. Our strategy is based on a classification of crystallographic space groups in six…

An algebraic classification of second order symmetric tensors in 5-dimensional Kaluza-Klein-type Lorentzian spaces is presented by using Jordan matrices. We show that the possible Segre types are $[1,1111]$, [2111], [311], [z,\bar{z},111],…

If a finite group of orientation-preserving diffeomorphisms of the 3-dimensional torus leaves invariant an oriented, closed, embedded surface of genus g>1 and preserves the orientation of the surface, then its order is bounded from above by…

The Turaev genus and dealternating number of a link are two invariants that measure how far away a link is from alternating. We determine the Turaev genus of a torus knot with five or fewer strands either exactly or up to an error of at…

We prove that rational homology of the Torelli group of genus g is infinite dimensional, provided g>6. This means that rational homology of the Torelli space of genus g>6 is infinite dimensional. The Torelli groups with marked points are…

We introduce and study the category of modular (i.e. with coefficient of positive characteristic) monodromic perverse sheaves on complex stratified $T$-varieties, with $T$ a complex algebraic torus. In particular, we show that under…

We define and study categories of singular Soergel bimodules, which are certain natural generalisations of Soergel bimodules. Indecomposable singular Soergel bimodules are classified, and we conclude that the split Grothendieck group of the…