Related papers: Density of integral points on algebraic varieties
We study Lelong numbers and integrability indices for $S^1$-invariant singular metrics on vector bundles over the disk.
Let G be a semisimple group over rational numbers and H is a subgroup over rational numbers. Given a representation of G and an integral vector x whose stabilizer is equal to H. In this paper we investigate the asymptotic of integral points…
Nested Archimedean copulas recently gained interest since they generalize the well-known class of Archimedean copulas to allow for partial asymmetry. Sampling algorithms and strategies have been well investigated for nested Archimedean…
We define four different kinds of multiplicity of an invariant algebraic curve for a given polynomial vector field and investigate their relationships. After taking a closer look at the singularities and at the line of infinity, we improve…
In this paper, we study the differential smoothness of diffusion algebras.
In this paper we investigate the distribution of the set of values of a linear map at integer points on a quadratic surface. In particular, it is shown that subject to certain algebraic conditions, this set is equidistributed. This can be…
This is a survey on the finite basis problem for varieties of algebraic systems. Our exposition is in two directions: (i) We give numerous examples of varieties which are not finitely based. (ii) We give examples of important varieties with…
We study the homogeneous involutions on the full square matrices over an algebraically closed field endowed with a division grading with commutative support. We obtain the classification of the isomorphism and equivalence classes for the…
A survey on recent developments in (algebraic) integral geometry is given. The main focus lies on algebraic structures on the space of translation invariant valuations and applications in integral geometry.
Using the index theory of seaweed algebras, we explore various new integer partition statistics. We find relations to some well-known varieties of integer partitions as well as a surprising periodicity result.
Particles with density different from that of the advecting turbulent fluid cluster due to the different response of light/heavy particles to turbulent fluctuations. This study focuses on the quantitative characterization of the segregation…
We study varieties defined over nonstandard fields using techniques of nonstandard mathematics.
We survey on algebraically elliptic varieties in the sense of Gromov.
We study the density of everywhere locally soluble diagonal quadric surfaces, parameterised by rational points that lie on a split quadric surface.
In this paper, we give the rigidity theorem for a log morphism as an extension of a fixed scheme morphism. We also give several applications of the rigidity theorem.
This is an exposition of a class of problems and results on the number of integral points close to plane curves. We give a detailed proof of a theorem of Huxley and Sargos, following the account of Bordell\`es. Along the way we correct an…
We exhibit invariants of smooth projective algebraic varieties with integer values, whose nonvanishing modulo p prevents the existence of an action without fixed points of certain finite p-groups. The case of base fields of characteristic p…
In this note, we announce results on integral points on some modular varieties, based on a generalisation of Runge's method in higher dimensions which will be explained beforehand. In particular, we obtain an explicit result in the case of…
We study the loci of principally polarized abelian varieties with points of high multiplicity on the theta divisor. Using the heat equation and degeneration techniques, we relate these loci and their closures to each other, as well as to…
We study the singularities of the projective dual variety.