Linearity conditions on the Jacobian ideal and logarithmic--meromorphic comparison for free divisors

Jacobian of meromorphic curves

The contact structure of two meromorphic curves gives a factorization of their jacobian.

Jacobian pairs

We study meromorphic jacobian pairs, i.e., pairs of polynomials in one variable, with coefficients meromorphic series in a second variable, whose jacobian relative to the two variables depends only on the second variable. We pose two meromorphic jacobian conjectures about such pairs, one of which is in terms of an invariant of the pair which we call the beta invariant. These conjectures are shown to imply the bivariate algebraic jacobian conjecture which predicts that two bivariate polynomials generate the polynomial ring if their jacobian is a nonzero constant. As another technique for studyi…

The skeleton of the Jacobian, the Jacobian of the skeleton, and lifting meromorphic functions from tropical to algebraic curves

Let K be an algebraically closed field which is complete with respect to a nontrivial, non-Archimedean valuation and let Λbe its value group. Given a smooth, proper, connected K-curve X and a skeleton Γof the Berkovich analytification X^\an, there are two natural real tori which one can consider: the tropical Jacobian Jac(Γ) and the skeleton of the Berkovich analytification Jac(X)^\an. We show that the skeleton of the Jacobian is canonically isomorphic to the Jacobian of the skeleton as principally polarized tropical abelian varieties. In addition, we show that the tropicalization of a classic…

与有两个无穷远点的双曲曲线相关的Sigma函数

Sigma function associated with a hyperelliptic curve with two points at infinity

本文研究了与有两个无穷远点的双曲曲线相关的Baker函数的性质，构造了一个整个函数，并用Riemannθ函数表示其。