On arc-analytic functions definable by a Weierstrass system
This paper presents certain characterizations through blowing up of arc-analytic functions definable by a convergent Weierstrass system closed under complexification.
On Bochner-Martinelli residue currents and their annihilator ideals
We study the residue current of Bochner-Martinelli type associated with a tuple of holomorphic germs at , whose common zero set equals the origin. Our main results are a geometric description of in terms of the Rees valuations associated with the ideal generated by and a characterization of when the annihilator ideal of equals .
On Equisingular Deformations of Cone-Like Surface Singularities.
On Plurigenera of Normal Isolated Singularities. I.
On Rational Singularities in Dimensions 2.
On Strict Levi q-Convexity and q-Concavity on Domains with Piecewise Smooth Boundaries.
On the Existence of Analytic Contractions.
On the Versal Resolutions of Deformations of Rational Double Points.
On the volume of a pseudo-effective class and semi-positive properties of the Harder-Narasimhan filtration on a compact Hermitian manifold
This paper divides into two parts. Let (X,ω) be a compact Hermitian manifold. Firstly, if the Hermitian metric ω satisfies the assumption that for all k, we generalize the volume of the cohomology class in the Kähler setting to the Hermitian setting, and prove that the volume is always finite and the Grauert-Riemenschneider type criterion holds true, which is a partial answer to a conjecture posed by Boucksom. Secondly, we observe that if the anticanonical bundle is nef, then for any ε >...