In the present paper, we make use of codes with good parameters and algebraic curves over finite fields with many rational points to construct dense packings of superballs. It turns out that our packing density is qui...In the present paper, we make use of codes with good parameters and algebraic curves over finite fields with many rational points to construct dense packings of superballs. It turns out that our packing density is quite reasonable. In particular, we improve some values for the best-known lower bounds on packing density.展开更多
In this paper, we study the intersection multiplicity of algebraic curves at a point both in R^2 and in real projective plane P^2. We introduce the fold point of curves and provide conditions for the relations between...In this paper, we study the intersection multiplicity of algebraic curves at a point both in R^2 and in real projective plane P^2. We introduce the fold point of curves and provide conditions for the relations between the intersection multiplicity of curves at a point and the folds of the point.展开更多
Let X be a generic smooth irreducible complex projective curve of genus g with g≥4. In this paper, we generalize the existence theorem of special divisors to high dimensional indecomposable vector bundles. We give a ...Let X be a generic smooth irreducible complex projective curve of genus g with g≥4. In this paper, we generalize the existence theorem of special divisors to high dimensional indecomposable vector bundles. We give a necessary and sufficient condition on the existence of n-dimensional indecomposable vector bundles E on X with det(E)=d, dim H^0(X,E)≥h. We also determine under what condition the set of all such vector bundles will be finite and how many elements it contains.展开更多
Here we study multiple coverings of rational and irational curves. We give a theorem about the non-gap sequence on m-gonal curves. We then study general irrational covering f ： X→ C, and say when h^0（X, f^＊（L））...Here we study multiple coverings of rational and irational curves. We give a theorem about the non-gap sequence on m-gonal curves. We then study general irrational covering f ： X→ C, and say when h^0（X, f^＊（L）） = h^0（C,L） for L line bundle on C.展开更多
The authors discuss the existence and classification of stable vector bundles of rank 3, with 2 3 or 4 linearly independent holomorphic sections. The sets of all such bundles are denoted by ω3^2,d and w3 respectivel...The authors discuss the existence and classification of stable vector bundles of rank 3, with 2 3 or 4 linearly independent holomorphic sections. The sets of all such bundles are denoted by ω3^2,d and w3 respectively. Our argument leads to sufficient and necessary conditions for the existence of both kinds of bundles. The conclusion is very interesting because of its contradiction to the conjectured dimension formula of stable bundles. Finally, we give a preliminary classification of ω3^2,4 and a complete discussion on the structure of ω3^3,2/3g＋2.展开更多
文摘In this paper, we characterize the commutant of Toeplitz operators on weighted Bergman space with symbol polynomial by using algebraic curves theory.
基金National Scientific Research Project 973 of China 2004CB318000
文摘In the present paper, we make use of codes with good parameters and algebraic curves over finite fields with many rational points to construct dense packings of superballs. It turns out that our packing density is quite reasonable. In particular, we improve some values for the best-known lower bounds on packing density.
基金Teaching reform research project of Shandong vocational education(2017228)
文摘In this paper, we study the intersection multiplicity of algebraic curves at a point both in R^2 and in real projective plane P^2. We introduce the fold point of curves and provide conditions for the relations between the intersection multiplicity of curves at a point and the folds of the point.
基金Project partly supported by the National Natural Science Foundation of China
文摘Let X be a generic smooth irreducible complex projective curve of genus g with g≥4. In this paper, we generalize the existence theorem of special divisors to high dimensional indecomposable vector bundles. We give a necessary and sufficient condition on the existence of n-dimensional indecomposable vector bundles E on X with det(E)=d, dim H^0(X,E)≥h. We also determine under what condition the set of all such vector bundles will be finite and how many elements it contains.
基金MIUR and GNSAGA of INdAM(Italy)Korea Research Foundation # 2005-070-C00005National Institute for Mathematical Sciences,Republic of Korea
文摘Here we study multiple coverings of rational and irational curves. We give a theorem about the non-gap sequence on m-gonal curves. We then study general irrational covering f ： X→ C, and say when h^0（X, f^＊（L）） = h^0（C,L） for L line bundle on C.
文摘The authors discuss the existence and classification of stable vector bundles of rank 3, with 2 3 or 4 linearly independent holomorphic sections. The sets of all such bundles are denoted by ω3^2,d and w3 respectively. Our argument leads to sufficient and necessary conditions for the existence of both kinds of bundles. The conclusion is very interesting because of its contradiction to the conjectured dimension formula of stable bundles. Finally, we give a preliminary classification of ω3^2,4 and a complete discussion on the structure of ω3^3,2/3g＋2.
