The Hartogs extension phenomenon in toric varieties

The Hartogs phenomenon in almost homogeneous varieties

We study the Hartogs extension phenomenon in noncompact almost homogeneous algebraic varieties and we prove the cohomological and weight criteria for the Hartogs phenomenon. In the case of spherical varieties, we prove a criterion for the Hartogs phenomenon in terms of colored fans.

哈托格斯现象与开嵌入、真映射、紧化及上同调

Hartogs and open embeddings, proper maps, compactifications, cohomologies

本文研究复解析簇上全纯向量丛全纯截面的哈托格斯延拓现象，分析其与开嵌入等结构及上同调的关系，还给出复近齐次代数G-簇（G为半阿贝尔簇）哈托格斯现象的凸几何判别准则。

Concavity, Abel-transform and the Abel-inverse theorem in smooth complete toric varieties

We extend the usual projective Abel-Radon transform to the larger context of a smooth complete toric variety X. We define and study toric concavity attached to an algebraic splitting vector bundle on X and we prove a toric version of the Abel-inverse theorem.