Interpolation for Curves in Projective Space with Bounded Error
Interpolation for Curves in Projective Space with Bounded Error
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具有有限误差的射影空间中的曲线插值
DOI：
10.1093/imrn/rnz136
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发表时间：
2019
影响因子：
1
通讯作者：
Larson, Eric
中科院分区：
文献类型：
--
作者：
Larson, Eric
Givengeneral pointsit is natural to ask whether there is a curve of given degreeand genuspassing through them; by counting dimensions a natural conjecture is that such a curve exists if and only if $$\begin{equation*}n \leq \left\lfloor \frac{(r + 1)d - (r - 3)(g - 1)}{r - 1}\right\rfloor.\end{equation*}$$The case of curves withnonspecialhyperplane section was recently studied in , where the above conjecture was shown to hold with exactly three exceptions.In this paper, we prove a “bounded-error analog” forspeciallinear series on general curves; more precisely we show that existence of such a curve subject to the stronger inequality $$\begin{equation*}n \leq \left\lfloor \frac{(r + 1)d - (r - 3)(g - 1)}{r - 1}\right\rfloor - 3.\end{equation*}$$Note that thecannot be replaced withwithout introducing exceptions (as a canonical curve incan only pass through nine general points, while a naive dimension count predicts twelve).We also use the same technique to prove that the twist of the normal bundlesatisfies interpolation for curves whose degree is sufficiently large relative to their genus, and deduce from this that the number of general points contained in the hyperplane section of a general curve is at least $$\begin{equation*}\min\left(d, \frac{(r - 1)^2 d - (r - 2)^2 g - (2r^2 - 5r + 12)}{(r - 2)^2}\right).\end{equation*}$$As explained in , these results play a key role in the author’s proof of the maximal rank conjecture .
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DOI：
--
发表时间：
1989
期刊：
影响因子：
--
作者：
J. Stevens
通讯作者：
J. Stevens
DOI：
--
发表时间：
2015
期刊：
影响因子：
--
作者：
Eric Larson
通讯作者：
Eric Larson
DOI：
10.1112/jlms.12451
发表时间：
2021
期刊：
Journal of the London Mathematical Society
影响因子：
--
作者：
Larson, Eric
通讯作者：
Larson, Eric
曲线上的插值和向量束
DOI：
--
发表时间：
2014
期刊：
影响因子：
--
作者：
A. Atanasov
通讯作者：
A. Atanasov