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Little is known about the behaviour of the Oka property of a complex manifold with respect to blowing up a submanifold. A manifold is of Class A if it is the complement of an algebraic subvariety of codimension at least 2 in an algebraic manifold that is Zariski-locally isomorphic to C n. A manifold of Class A is algebraically subelliptic and hence Oka, and(More)
For a q × q matrix x = (x i,j) we let J(x) = (x −1 i,j) be the Hadamard inverse, which takes the reciprocal of the elements of x. We let I(x) = (x i,j) −1 denote the matrix inverse, and we define K = I • J to be the birational map obtained from the composition of these two involutions. We consider the iterates K n = K • · · · • K and determine degree(More)
Let K be an algebraically closed field, X a smooth projective variety over K and f : X → X a dominant regular morphism. Let N i (X) be the group of algebraic cycles modulo numerical equivalence. Let χ(f) be the spectral radius of the pullback f * : H * (X, Q l) → H * (X, Q l) on l-adic cohomology groups, and λ(f) the spectral radius of the pullback f * : N(More)
We obtain some two-bound estimates for the local growth of pluri-subharmonic functions. We propose a conjecture which is similar to the comparison theorem in [H. Alexander and B. A. Taylor, Comparison of two capacities in C n , Math. Z. 186 (1984), 407–417]. We verify this conjecture in several cases. We then show that this conjecture implies extensions of(More)
We continue the work of [14]. Let E be a non-Blaschke subset of the unit disc D of the complex plane C. Fixed 1 ≤ p ≤ ∞, let H p (D) be the Hardy space of holomorphic functions in the disk whose boundary value function is in L p (∂D). Fixed 0 < R < 1. For ǫ > 0 define Cp(ε, R) = sup{ sup |z|≤R |g(z)| : g ∈ H p , gp ≤ 1, |g(ζ)| ≤ ε ∀ζ ∈ E}. In this paper we(More)
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