Related papers: Universal torsors and Cox rings

We extend the infinitesimal Torelli theorem for smooth hypersurfaces to nodal hypersurfaces.

We examine a few problems of enumerative geometry and present their solutions in the framework of deformed (quantum) cohomology rings.

In the toric variety $\mathcal{T}$, with Cox ring graded by $\deg(z_{2i})=(1,-1,0)$, $\deg(z_{2i+1})=(1,0,-1)$ and $\deg(w_\pm)=(0,1,0),(0,0,1)$, we study hypersurfaces $\widetilde{X}^{2n}\subset\mathcal T$ of multidegree $(2d+1,-d,-d)$…

In the present study we consider the generalized rotational surfaces in Euclidean spaces. Firstly, we consider generalized spherical curves in Euclidean $(n+1)-$space $\mathbb{E}^{n+1}$. Further, we introduce some kind of generalized…

The aim of this paper is to present a construction of smooth rational surfaces in projective fourspace with degree 12 and sectional genus 13. The construction is based on exterior algebra methods, finite field searches and standard…

We consider ruled surfaces with finite multiplicity. We study behaviors of the striction curves and the singularities of the ruled surfaces. We also give geometric meanings of invariants related to the ruled surfaces.

In this paper we classify certain special ruled surfaces in $\R^3$ under the general theorem of characterization of constant angle surfaces. We study the tangent developable and conical surfaces from the point of view the constant angle…

We study various aspects of the dynamics induced by integer matrices on the invariant rational lattices of the torus in dimension 2 and greater. Firstly, we investigate the orbit structure when the toral endomorphism is not invertible on…

This paper is a survey on universal algorithms for solving the matrix Bellman equations over semirings and especially tropical and idempotent semirings. However, original algorithms are also presented. Some applications and software…

This text gives some results about quantum torsors. Our starting point is an old reformulation of torsors recalled recently by Kontsevich. We propose an unification of the definitions of torsors in algebraic geometry and in Poisson…

We discuss various phenomena of tangency in projective and convex geometry.

We classify rational surfaces for which the image of the automorphisms group in the group of linear transformations of the Picard group is the largest possible. This answers a question raised by Arthur Coble in 1928, and can be rephrased in…

We provide new logarithmic lower bounds for the torsion order of a very general complete intersection in projective space as well as a very general hypersurface in products of projective spaces and Grassmannians, in particular we prove…

We show that a very general Jacobian elliptic surface is determined by its polarized rational Hodge structure, subject to various constraints on the irregularity and the geometric genus.

We give an explicit presentation of the integral Chow ring of a stack of smooth plane cubics. We also determine some relations in the general case of hypersurfaces of any dimension and degree.

The purpose of this paper is to give a "down--to--earth" proof of the well--known fact that a randomly chosen elliptic curve over the rationals is most likely to have trivial torsion.

We obtain bounds on the number of maximal torsion cosets for algebraic subvarieties of n-tori, defined over the rationals, using model theoretic methods.

An overview of the cosmological models with expansion, shear and rotation is presented. Problems of the rotating models are discussed, their general kinematic properties and dynamical realizations are described. A particular attention is…

In this paper, we prove three related results; (1) Extension of our result in [10] to all generic hypersurfaces. More precisely, the normal sheaf of a generic rational map $c_0$ to a generic hypersurface $X_0$ of $\mathbf P^n, n\geq 4$ has…

We systematically determine the regular representations, quivers and representation type of all liftings of two-dimensional quantum linear spaces.