论文标题
投影空间的某些嵌入的方程式到另一个
Equations of some embeddings of a projective space into another one
论文作者
论文摘要
在Arxiv：Math/0405373中，Eisenbud，Huneke和Ulrich猜想了Castelnuovo-Mummford的结果，该结果是嵌入一个投射空间$ \ MATHBB {p}^{n-1}^{n-1} \ qugineRectRightArrow \ qugineRectRarow \ qugindrightArrow \ Mathbb \ Mathbb {p} p}^r-1} $ linear in linear in linears的嵌入$ \ mathfrak {m} $ - 主要理想。该结果特别意味着图像是由$ n $最多由学位方程定义的方案。在本文中，我们证明了与输入理想相关的Jacobian双基质的最大未成年人的理想，将图像定义为一个方案。它以$ n $为单位生成。表明该理想具有线性分辨率将暗示Arxiv中的猜想：MATH/0405373。此外，如果这种未成年人的理想与度$ n $中的图像之一相吻合 - 我们希望是真实的，那么该理想最大未成年人的分辨率的线性等同于Arxiv中的猜想：Math/0405373。
In arXiv:math/0405373 , Eisenbud, Huneke and Ulrich conjectured a result on the Castelnuovo-Mumford regularity of the embedding of a projective space $\mathbb{P}^{n-1}\hookrightarrow \mathbb{P}^{r-1}$ determined by generators of a linearly presented $\mathfrak{m}$-primary ideal. This result implies in particular that the image is scheme defined by equations of degree at most $n$. In this text we prove that the ideal of maximal minors of the Jacobian dual matrix associated to the input ideal defines the image as a scheme; it is generated in degree $n$. Showing that this ideal has a linear resolution would imply that the conjecture in arXiv:math/0405373 holds. Furthermore, if this ideal of minors coincides with the one of the image in degree $n$ - what we hope to be true - the linearity of the resolution of this ideal of maximal minors is equivalent to the conjecture in arXiv:math/0405373.
