A Zariski dense exceptional set in Manin’s Conjecture: dimension 2

Bers Slices Are Zariski Dense

Each Bers slice is a holomorphically embedded copy of Teichmüller space within XC(S). While it follows that BY can be locally described as the common zero locus of finitely many analytic functions on XC(S), it is known that the Bers slice is not a locally algebraic set [DK]—this is used to show that W. Thurston’s skinning map is not a constant function [DK]. We prove a stronger result about the...

The Manin Conjecture in Dimension 2

Zariski Dense Random Walks on Homogeneous Spaces

A short proof of the maximum conjecture in CR dimension one

In this paper and by means of the extant results in the Tanaka theory, we present a very short proof in the specific case of CR dimension one for Beloshapka's maximum conjecture. Accordingly, we prove that each totally nondegenerate model of CR dimension one and length >= 3 has rigidity. As a result, we observe that the group of CR automorphisms associated with each of such models contains onl...

Matrices similar on a Zariski - open set

1. Introduction ,(1.1) Let A, B be n x n matrices whose elements are functions holomorphic in a connected open subset V of the complex plane. The matrices A, Bare called pointwise similar on V if for each XE V there exists a non-singular n x n matrix C x with complex elements such that B(x) = C;;l A (x) Cx' They are holomorphically similar on V if there exists a matrix C of functions holomorphi...