Related papers: On plane sextics with double singular points

We generalize the notions of singularities and ordinary points from linear ordinary differential equations to D-finite systems. Ordinary points of a D-finite system are characterized in terms of its formal power series solutions. We also…

Finite groups with given systems of permuteral and strongly permuteral subgroups are studied. New characterizations of w-supersoluble and supersoluble groups are received.

A necessary condition for uniqueness of factorizations of elements of a finite group $G$ with factors belonging to a union of some conjugacy classes of $G$ is given. This condition is sufficient if the number of factors belonging to each…

We propose a geometric explanation for the observation that generic quadratic polynomials over split quaternions may have up to six different factorizations while generic polynomials over Hamiltonian quaternions only have two. Split…

We prove several results concerning genus numbers of quintic fields: we compute the proportion of quintic fields with genus number one; we prove that a positive proportion of quintic fields have arbitrarily large genus number; and we…

We show the existence of sextics of non-torus type which is a Zariski partner of the tame sextics of torus type with simple singularities.

Using the structure of the jet schemes of rational double point singularities, we construct "minimal embedded toric resolutions" of these singularities. We also establish, for these singularities, a correspondence between a natural class of…

We show, in this second part, that the maximal number of singular points of a quartic surface $X \subset \mathbb{P}^3_K$ defined over an algebraically closed field $K$ of characteristic 2 is at most 14, and that, if we have 14…

We show that the maximal number of singular points of a normal quartic surface $X \subset \mathbb{P}^3_K$ defined over an algebraically closed field $K$ of characteristic $2$ is at most $20$, and that if equality is attained, then the…

We consider a planar doublebox with four massive external momenta and two massive internal propagators. We derive the system of differential equations for the relevant master integrals, cast it in canonical form, write it as a $d\log$ form…

We show that the maximal number of singular points of a normal quartic surface $X \subset \mathbb{P}^3_K$ defined over an algebraically closed field $K$ of characteristic 2 is at most 12, if the minimal resolution of $X$ is not a…

We classify, up to some lattice-theoretic equivalence, all possible configurations of rational double points that can appear on a surface whose minimal resolution is a complex Enriques surface.

We construct the first examples of what we call fake ES-irreducible components; Definition 2.8. In our way to do so, we classify the automorphism groups of smooth plane sextics that only have automorphisms of order 3 or less; Theorems 2.1,…

We study supersolvable line arrangements in ${\mathbb P}^2$ over the reals and over the complex numbers, as the first step toward a combinatorial classification. Our main results show that a nontrivial (i.e., not a pencil or near pencil)…

We study singularities obtained by the contraction of the maximal divisor in compact (non kaehlerian) surfaces which contain global spherical shells. These singularities are of genus 1 or 2, may be Q-Gorenstein, numerically Gorenstein or…

We establish a one-to-one correspondence between the singularity categories of rational double points and the simply-laced Dynkin graphs in arbitrary characteristic. This correspondence is well-known in characteristic zero since the…

The main aim of this article is to study the quantitative structure of projective symplectic groups $PSp_{4}(q)$ with $q>2$ even. Indeed, we prove that the groups $PSp_{4}(q)$ with $q>2$ even are uniquely determined by their orders and the…

We effectively bound T-singularities on non-rational projective surfaces with an arbitrary amount of T-singularities and ample canonical class. This fully generalizes the previous work for the case of one singularity, and illustrates the…

We construct quantization of semisimple conjugacy classes of the exceptional group $G=G_2$ along with and by means of their exact representations in highest weight modules of the quantum group $U_q(\mathfrak{g})$. With every point $t$ of a…

For an isolated hypersurface singularity which is neither simple nor simple elliptic, it is shown that there exists a distinguished basis of vanishing cycles which contains two basis elements with an arbitrary intersection number. This…