相关论文: Universal torsors and Cox rings

Deformational structures, in many aspects generalizing standard elasticity theory, are investigated in abstract form. Within free deformational structures we define algebra of deformations, classify them by its special properties, define…

Let $A$ be an abelian surface over $\mathbb{Q}$ whose geometric endomorphism ring is a maximal order in a non-split quaternion algebra. Inspired by Mazur's theorem for elliptic curves, we show that the torsion subgroup of $A(\mathbb{Q})$ is…

We study groups, exponential groups and ordered groups equipped with valuations. We investigate algebraic and topological features of such valued structures, and apply our findings in order to solve regular equations over groups using…

We classify the smooth Fano 4-folds of Picard number two that have a general hypersurface Cox ring.

We introduce a framework for coverings of noncommutative spaces. Moreover, we study noncommutative coverings of irrational quantum tori and characterize all such coverings that are connected in a reasonable sense.

Given a generic totally real torus unknotted in the unit sphere of the complex plane, we prove the following alternative : either there exists a filling of the torus by holomorphic discs and the torus is rationally convex, or its rational…

We present an algorithm for computing curves and families of curves of prescribed degree and geometric genus on real rational surfaces.

One of the most powerful ideas in the study and classification of algebraic varieties is the notion of a model: that is, to single out an object, in the appropriate isomorphism class, with nice properties. This survey aims to define and…

We study rationality properties of real singular cubic threefolds.

We study the arithmetic of Enriques surfaces whose universal covers are singular K3 surfaces. If a singular K3 surface X has discriminant d, then it has a model over the ring class field d. Our main theorem is that the same holds true for…

The aim of this paper is to study the group of isomorphism classes of torsors of finite flat group schemes of rank 2 over a commutative ring $R$. This, in particular, generalises the group of quadratic algebras (free or projective), which…

In this paper uniformly rotating relativistic rings are investigated analytically utilizing two different approximations simultaneously: (1) an expansion about the thin ring limit (the cross-section is small compared with the size of the…

We study parallel surfaces and dual surfaces of cuspidal edges. We give concrete forms of principal curvature and principal direction for cuspidal edges. Moreover, we define ridge points for cuspidal edges by using those. We clarify…

In this paper we study the possible torsions of elliptic curves over $\mathbb Q(i)$ and $\mathbb Q(\sqrt {-3})$.

In this paper I consider the polymorpism of representations of universal algebra and tensor product of representations of universal algebra.

A Roche model for describing uniformly rotating rings is presented and the results are compared with numerical solutions to the full problem for polytropic rings. In the thin ring limit, the surfaces of constant pressure including the…

We study some topological properties of attractors.

We prove that the orbit closure of the determinant is not normal. A similar result is obtained for the orbit closure of the permanent multiplied by a power of a linear form.

We prove Manin's conjecture for four singular quartic del Pezzo surfaces over imaginary quadratic number fields, using the universal torsor method.

We study relations of some classes of $k$-convex, $k$-visible bodies in Euclidean spaces. We introduce and study \textrm{circular projections} in normed linear spaces and classes of bodies related with families of such maps, in particular,…