论文标题
非射影曲线的距离偏度品种的奇异性和syzygies
Singularities and syzygies of secant varieties of nonsingular projective curves
论文作者
论文摘要
近年来，定义Scant品种及其Syzygies的方程式引起了极大的关注。本文的目的是通过解决几个猜想并揭示奇异性与Syzygies之间的相互作用来对偏度曲线的详细研究进行详尽的研究。主要结果断言，如果非负整数$ k $ $ k $和$ p $的非单词曲线的嵌入线束大于$ 2g+2k+p $，那么$ k $ thec $ thec $ the corve cohen-cohen-macaulay and propelly $ n proptiality cohen-macaulay and proptials $ n;此外，根据曲线的属进一步对距离品种的奇异性进一步分类，并且也获得了Castelnuovo-穆姆福德的规律性。作为主要技术成分之一，我们在曲线的笛卡尔产品上建立了一个消失的定理，该定理可能具有独立的兴趣，并可能在其他地方找到应用。
In recent years, the equations defining secant varieties and their syzygies have attracted considerable attention. The purpose of the present paper is to conduct a thorough study on secant varieties of curves by settling several conjectures and revealing interaction between singularities and syzygies. The main results assert that if the degree of the embedding line bundle of a nonsingular curve of genus $g$ is greater than $2g+2k+p$ for nonnegative integers $k$ and $p$, then the $k$-th secant variety of the curve has normal Du Bois singularities, is arithmetically Cohen--Macaulay, and satisfies the property $N_{k+2, p}$. In addition, the singularities of the secant varieties are further classified according to the genus of the curve, and the Castelnuovo--Mumford regularities are also obtained as well. As one of the main technical ingredients, we establish a vanishing theorem on the Cartesian products of the curve, which may have independent interests and may find applications elsewhere.
