Shanyu Ji

A global Łojasiewicz inequality for algebraic varieties

Let X be the locus of common zeros of polynomials f 1 ,..., f κ in n complex variables. A global upper bound for the distance to X is given in the form of a Lojasiewicz inequality. The exponent in this inequality is bounded by d min(n,k) where d=max(3, deg f i ). The estimates are also valid over an algebraically closed field of any characteristic

Properties of compact complex manifolds carrying closed positive currents

We show that a compact complex manifold is Moishezon if and only if it carries a strictly positive, integral (1, 1)-current. We then study holomorphic line bundles carrying singular hermitian metrics with semi-positive curvature currents, and we give some cases in which these line bundles are big. We use these cases to provide sufficient conditions for a compact complex manifold to be Moishezon in terms of the existence of certain semi-positive, integral (1,1)-currents. We also show that the intersection number of two closed semi-positive currents of complementary degrees on a compact complex manifold is positive when the intersection of their singular supports is contained in a Stein domain.

On the Riemann mapping theorem

We prove a generalization of the Riemann mapping theorem: if a bounded simply connected domain Q with connected smooth boundary has the spherical boundary, then it is biholomorphic to the unit ball.

An example of a real analytic strongly pseudoconvex hypersurface which is not holomorphically equivalent to any algebraic hypersurface

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Flatness of CR submanifolds in a sphere

AbstractIn Euclidean geometry, for a real submanifold M in

Nevanlinna Inequality For Intersection of Divisors

\mathbb{E}^{n + a}

A new gap phenomenon for proper holomorphic mappings from

, M is a piece of