We introduce the notion of K-very smoothness which is a generalization of very smoothness in Banach spaces. A necessary and sufficient condition for a Banach space to be K-very smooth is obtained. We also consider som...We introduce the notion of K-very smoothness which is a generalization of very smoothness in Banach spaces. A necessary and sufficient condition for a Banach space to be K-very smooth is obtained. We also consider some relations between K-very smoothness and other geometrical notions.展开更多
We study the Cayley-Bacharach property on complex projective smooth varieties of dimension n≥2 for zero dimensional subscheme defined by the zero set of the wedge of r-n + 1 global sections of a rank r≥n vector bund...We study the Cayley-Bacharach property on complex projective smooth varieties of dimension n≥2 for zero dimensional subscheme defined by the zero set of the wedge of r-n + 1 global sections of a rank r≥n vector bundle,and give a construction of high rank reflexive sheaves and vector bundles from codimension 2 subschemes.展开更多
We will give optimal bounds for Seshadri constants of an ample line bundle at multiple points on a complex projective surface X.We also present a solution to the long-studied classical problem on the existence of curv...We will give optimal bounds for Seshadri constants of an ample line bundle at multiple points on a complex projective surface X.We also present a solution to the long-studied classical problem on the existence of curves on X with given topological singularities at r arbitrary points p1,...,pr.Namely,we obtain a universal lower bound on the degree of curves for the existence.It is independent of the position of the singular points.展开更多
文摘We introduce the notion of K-very smoothness which is a generalization of very smoothness in Banach spaces. A necessary and sufficient condition for a Banach space to be K-very smooth is obtained. We also consider some relations between K-very smoothness and other geometrical notions.
文摘We study the Cayley-Bacharach property on complex projective smooth varieties of dimension n≥2 for zero dimensional subscheme defined by the zero set of the wedge of r-n + 1 global sections of a rank r≥n vector bundle,and give a construction of high rank reflexive sheaves and vector bundles from codimension 2 subschemes.
基金supported by National Natural Science Foundation of China (Grant No.10731030)Science Foundations of the Education Ministry of China+1 种基金STCSM Foundation of Shanghaisupported by the Innovation Program of Shanghai Municipal Education Commission (GrantNo. 11ZZ18)
文摘We will give optimal bounds for Seshadri constants of an ample line bundle at multiple points on a complex projective surface X.We also present a solution to the long-studied classical problem on the existence of curves on X with given topological singularities at r arbitrary points p1,...,pr.Namely,we obtain a universal lower bound on the degree of curves for the existence.It is independent of the position of the singular points.
