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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Rational points and homogeneous spaces over function fields of curves
曲线函数场 有理点 齐次空间
2023/4/17
In the last decade, there has been a growing interest in the study of rational points on homogeneous spaces of linear algebraic groups defined over fields having good arithmetical properties other tha...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Number of rational points of difference varieties in finite difference fields
有限差分域 差分簇 有理点数
2023/4/13
A difference field is a field with a distinguished automorphism. Automorphisms of a finite field are powers of the Frobenius map. In this talk, I will discuss how to estimate the number of rational po...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：μ-basis for a tensor product rational surface with respect to one variable
张量积 有理曲面 变量 μ基
2023/4/28
The method of moving planes and moving quadrics expresses the implicit equation of a rational parametric surface as a compact determinant. Efficient computation of the moving planes and moving quadric...
Given a sequence {αn} in (0, 1) converging to a rational, we examine
the model theoretic properties of structures obtained as limits of ShelahSpencer
graphs G(m, m−αn ). We show that in most c...
A proof of Thurston's topological characterization of rational functions
Thurston's topological characterization rational functions
2015/8/26
The criterion proved in this paper was stated by Thurston in November 1982. Thurston lectured on its proof on several occasions, notably at the NSF summer conference inDuluth, 1983, where one of the a...
In this paper, a geometric interpretation is provided of a new rational Landen transformation. The convergence of its iterates is also established.
THE ENUMERATIVE GEOMETRY OF RATIONAL AND ELLIPTIC CURVES IN PROJECTIVE SPACE
ELLIPTIC CURVES PROJECTIVE SPACE
2015/7/14
We study the geometry of moduli spaces of genus 0 and 1 curves in Pn with
speci ed contact with a hyperplane H. We compute intersection numbers on these spaces that
correspond to the number of degre...
Caporaso and Harris derive recursive formulas counting nodal plane
curves of degree d and geometric genus g in the plane (through the appropriate number of xed
general points). We rephrase their ar...
TWELVE POINTS ON THE PROJECTIVE LINE, BRANCHED COVERS, AND RATIONAL ELLIPTIC FIBRATIONS
PROJECTIVE LINE BRANCHED COVERS
2015/7/14
The following divisors in the space Sym12 P1 of twelve points on
P1 are actually the same: (A) the possible locus of the twelve nodal bers in
a rational elliptic bration (i.e. a pencil of plane cu...
INVOLUTIVE RATIONAL NORMAL STRUCTURES.
Twisted Weyl Group Multiple Dirichlet Series Over the Rational Function Field
Rational Function Field Multiple Dirichlet
2014/12/8
Let K be a global field. For each prime p of K, the p-part of a multiple Dirichlet series defined over K is a generating function in several variables for the p-power coefficients. Let _ be an irreduc...
Locally harmonic Maass forms and rational period functions
hyperbolic Poincare series harmonic weak Maass forms cusp forms lifting maps Shimura lift Shintani lift
2012/6/21
In this paper we define a new type of modular object and construct explicit examples of such functions. Our functions are closely related to cusp forms constructed by Zagier which played an important ...
Quadratic congruences on average and rational points on cubic surfaces
Quadratic congruences rational points Manin’s conjecture cubic surfaces universal torsors
2012/5/24
We investigate the average number of solutions of certain quadratic congruences. As an application, we establish Manin's conjecture for a cubic surface whose singularity type is A_5+A_1.
Rational cubic fourfolds containing a plane with nontrivial Clifford invariant
Rational cubic fourfolds nontrivial Clifford invariant Algebraic Geometry
2012/5/9
We isolate a general class of smooth rational cubic fourfolds containing a plane whose associated quadric surface bundle does not have a rational section. Equivalently, the Brauer class of the even Cl...
Counting rational points over number fields on a singular cubic surface
rational points over number fields singular cubic surface Number Theory
2012/4/18
A conjecture of Manin predicts the distribution of K-rational points on certain algebraic varieties defined over a number field K. In recent years, a method using universal torsors has been successful...