Let C be a smooth projective curve over C, and K be the canonical line bundle. A well-known Theorem of Noether says that if C is not a hyperelliptic curve, then the map H^o(C,K)(?)H^o(C,K)→H^o(C, 2K) is surjective,wh...Let C be a smooth projective curve over C, and K be the canonical line bundle. A well-known Theorem of Noether says that if C is not a hyperelliptic curve, then the map H^o(C,K)(?)H^o(C,K)→H^o(C, 2K) is surjective,which means that K is normally generated.展开更多
ⅠConcerning the Clifford theorem with the stability of vector bundles, Arrondo-Sols proposed the following conjecture.Arrondo-Sols’Conjecture. Let E be a rank two vector bundle of degree d on a smooth complex algebr...ⅠConcerning the Clifford theorem with the stability of vector bundles, Arrondo-Sols proposed the following conjecture.Arrondo-Sols’Conjecture. Let E be a rank two vector bundle of degree d on a smooth complex algebraic curve of genus g, -e be the minimal self-intersection number of a unisecant curve in the ruled surface p(E), and r+ 1 =h^0(E). If -e≤d≤4g-4+e and E≠L⊕L,展开更多
文摘Let C be a smooth projective curve over C, and K be the canonical line bundle. A well-known Theorem of Noether says that if C is not a hyperelliptic curve, then the map H^o(C,K)(?)H^o(C,K)→H^o(C, 2K) is surjective,which means that K is normally generated.
基金Project partly supported by the National Natural Science Foundation of China and the Institute of Mathematics, Academia Sinica.
文摘ⅠConcerning the Clifford theorem with the stability of vector bundles, Arrondo-Sols proposed the following conjecture.Arrondo-Sols’Conjecture. Let E be a rank two vector bundle of degree d on a smooth complex algebraic curve of genus g, -e be the minimal self-intersection number of a unisecant curve in the ruled surface p(E), and r+ 1 =h^0(E). If -e≤d≤4g-4+e and E≠L⊕L,
