相关论文: Rational Points on Weighted projective Spaces
In this article, firstly, some simple and smoothness properties of the weighted numerical radius and the weighted Crawford number functions are investigated. Then, some generalization formulas for lower and upper bounds of the weighted…
This paper develops asymptotic methods to count faces of random high-dimensional polytopes. Beyond its intrinsic interest, our conclusions have surprising implications - in statistics, probability, information theory, and signal processing…
We derive asymptotic formulas for the number of rational points on a smooth projective quadratic hypersurface of dimension at least three inside of a shrinking adelic open neighbourhood. This is a quantitative version of weak approximation…
We relate the problem of counting number fields, in particular, Malle's conjecture with the problem of counting rational points on singular Fano varieties, in particular, Batyrev and Tschinkel's generalization of Manin's conjecture.
We prove an upper bound for the number of rational points of bounded height in a weighted projective stack which lie in a given thin subset. As a consequence, we show that $100\%$ of hyperelliptic curves do not admit a prescribed on-trivial…
These notes provide a description of the abelian categories that arise as categories of coherent sheaves on weighted projective lines. Two different approaches are presented: one is based on a list of axioms and the other yields a…
We determine upper bounds on the number of rational points of an affine or projective algebraic set defined over an extension of a finite field by a system of polynomial equations, including the case where the algebraic set is not defined…
The closed span of Rademacher functions is investigated in the weighted spaces X(w), where X is a symmetric space on [0,1] and w is a positive measurable function on [0,1]. By using the notion and properties of the Rademacher multiplicator…
We describe weighted projective lines in the sense of Geigle and Lenzing by a moduli problem on the canonical algebra of Ringel. We then go on to study generators of the derived categories of coherent sheaves on the total spaces of their…
Given a projective intersection of two quadrics X in at least 9 variables, the quantitative behaviour of the rational points on X is investigated under the assumption that X contains a pair of conjugate singular points defined over the…
The notion of symmetry in polynomial rings with several indeterminates is generalized to polynomial rings over finite fields. Families of extensions of the projective line over a finite field of constants possessing this property are…
Regions-based theories of space aim -- among others -- to define points in a geometrically appealing way. The most famous definition of this kind is probably due to Whitehead. However, to conclude that the objects defined are points indeed,…
In this paper, we give a uniform upper bound on the rational points of bounded height provided by conics in a cubic surface. For this target, we give a generalized version of the global determinant method of Salberger by Arakelov geometry.
In this note, we provide explicit expressions for the projections onto the graph of a quadratic polynomial. The projections are obtained by examining the critical points of the associated quartic polynomial, that is, the roots of the cubic…
This paper is concerned with configurations of points in a plane lattice which determine angles that are rational multiples of $\pi$. We shall study how many such angles may appear in a given lattice and in which positions, allowing the…
We count rational points of bounded height on the non-normal senary quartic hypersurface x 4 = (y 2 1 + $\times$ $\times$ $\times$ + y 2 4)z 2 in the spirit of Manin's conjecture.
We introduce and investigate a weighted propositional configuration logic over commutative semirings. Our logic is intended to serve as a specification language for software architectures with quantitative features. We prove an efficient…
We study finite-dimensional spaces of rational one-forms on a projective manifold by means of their integrable locus.
Chen and Ruan [6] defined a very interesting cohomology theory for orbifolds, which is now called Chen-Ruan cohomology. The primary objective of this paper is to compute the Chen-Ruan cohomology rings of the weighted projective spaces, a…
In this note, we study linear determinantal representations of smooth plane cubics over finite fields. We give an explicit formula of linear determinantal representations corresponding to rational points. Using Schoof's formula, we count…