The Maximal Rank Conjecture for sections of curves
The Maximal Rank Conjecture for sections of curves
复制标题
曲线段的最大秩猜想
DOI：
10.1016/j.jalgebra.2020.03.006
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发表时间：
2020
影响因子：
0.9
通讯作者：
Larson, Eric
中科院分区：
文献类型：
--
作者：
Larson, Eric
Abstract Let C⊂ P r be a general curve of genus g embedded via a general linear series of degree d. The Maximal Rank Conjecture asserts that the restriction maps H 0 (O P r (m))→ H 0 (O C (m)) are of maximal rank; this determines the Hilbert function of C. In this paper, we prove an analogous statement for the union of hyperplane sections of general curves. More specifically, if H⊂ P r is a general hyperplane, and C 1, C 2,…, C n are general curves, we show H 0 (O H (m))→ H 0 (O (C 1∪ C 2∪⋯∪ C n)∩ H (m)) is of maximal rank, except for some counterexamples when m= 2. As explained in [5], this result plays a key role in the author's proof of the Maximal Rank Conjecture [7].
平滑代数空间曲线
DOI：
10.1007/bfb0074998
发表时间：
1985
期刊：
The Journal of organic chemistry
影响因子：
--
作者：
R. Hartshorne;A. Hirschowitz
通讯作者：
A. Hirschowitz
射影空间中一般曲线的嵌入：二次曲线的范围
影响因子：
0.4
作者：
E. Ballico
通讯作者：
E. Ballico