标题： 一般曲线在射影空间中的嵌入：二次曲线的范围 显示英文标题

标题： Embeddings of general curves in projective spaces: the range of the quadrics

摘要： 设$C \subset \mathbb {P}^r$为一个具有给定亏格的普通光滑曲线的给定次数的一般嵌入。 这里我们证明，要么$h^0(\mathbb {P}^r,\mathcal {I}_C(2)) =0$，要么$h^1(\mathbb {P}^r,\mathcal {I}_C(2)) =0$（一个问题称为二次型范围内的最大秩猜想）。 显示英文摘要

摘要： Let $C \subset \mathbb {P}^r$ a general embedding of prescribed degree of a general smooth curve with prescribed genus. Here we prove that either $h^0(\mathbb {P}^r,\mathcal {I}_C(2)) =0$ or $h^1(\mathbb {P}^r,\mathcal {I}_C(2)) =0$ (a problem called the Maximal Rank Conjecture in the range of quadrics).