A Note on the Geometry of Green-Lazarsfeld sets
We study some subsets of the Green-Lazarsfeld set $Σ^{1}(M)$ for a compact Kahler manifold $M$.
math.AG↗
arXiv subjects
A. Brudnyi
Publications and source records attributed to A. Brudnyi.
Solvable Quotients of Kahler Groups
We prove several results on the structure of solvable quotients of fundamental groups of compact Kahler manifolds (Kahler groups).
math.AG↗
A Uniqueness Property for H^{\infty} on Coverings of Projective Manifolds
Let Y be a regular covering of a complex projective manifold M\hookrightarrow CP^{N} of dimension n\geq 2. Let C be intersection with M of at most n-1 generic hypersurfaces of degree d in CP^{N}. The preimage X of C in Y is a connected submanifold. Let H^{\infty}(Y) and H^{\infty}(X) be the Banach spaces of bounded holomorphic functions on Y and X in the corresponding supremum norms. We prove that the restriction H^{\infty}(Y)\longrightarrow H^{\infty}(X) is an isometry for d large enough. This answers the question posed in [L] by F. Larusson and strengthen his example of the Riemann surface with large corona.
math.CV↗
The Distribution of Values of Analytic Functions on Convex Bodies
Proceeding the study of local properties of analytic functions started in [Br] we prove new dimensionless inequalities for such functions in terms of their Chebyshev degree. As a consequence, we obtain the reverse Holder inequalities for analytic functions with absolute (i.e., independent of dimension) constants. For polynomials such inequalities were recently proved by Bobkov who sharpened and generalized the previous Bourgain result and by Sodin and Volberg.
math.CV↗
A Tangential Markov Inequality on Exponential Curves
We show that on the curves y=e^{t(x)} where t(x) is a fixed polynomial, there holds a tangential Markov inequality of exponent four. Specifically, for the real interval [a,b] there is a constant C such that max_{x\in [a,b]}|\frac{d}{dx}P(x,e^{t(x)})|\leq C(deg(P))^{4} max_{x\in [a,b]}|P(x,e^{t(x)})| for all bivariate polynomials P(x,y).
math.CV↗
Triangular de Rham Cohomology of Compact Kahler Manifolds
We study the de Rham 1-cohomology H^1_{DR}(M,G) of a smooth manifold M with values in a Lie group G. By definition, this is the quotient of the set of flat connections in the trivial principle bundle $M\times G$ by the so-called gauge equivalence. We consider the case when M is a compact Kähler manifold and G is a solvable complex linear algebraic group of a special class which contains the Borel subgroups of all complex classical groups and, in particular, the group $T_n(\Bbb C)$ of all triangular matrices. In this case, we get a description of the set H^1_{DR}(M,G) in terms of the 1-cohomology of M with values in the (abelian) sheaves of flat sections of certain flat Lie algebra bundles with fibre $\frak g$ (the Lie algebra of G) or, equivalently, in terms of the harmonic forms on M representing this cohomology.
math.DG↗