论文标题
表面反示例对艾森布德·古特的猜想
Surface counterexamples to the Eisenbud-Goto conjecture
论文作者
论文摘要
众所周知，对于算术上的Cohen-Macaulay品种，投射曲线，光滑的表面，$ \ Mathbb {p}^5 $中的平滑三倍，以及Codioimension二的三倍品种。在J. McCullough和I. Peeva在2018年构建了反例之后，找到Eisenbud-Goto猜想的类别是一个有趣的问题。到目前为止，尚未找到表面反例，而知道更大或等于3的任何尺寸的反例。 在本文中，我们构建了$ \ mathbb {p}^4 $投影表面的Eisenbud-Goto猜想，并研究投影性不变性，共同体学特性和几何特性。反例是通过投影空间之间的二项式有理图构建的。
It is well known that the Eisenbud-Goto regularity conjecture is true for arithmetically Cohen-Macaulay varieties, projective curves, smooth surfaces, smooth threefolds in $\mathbb{P}^5$, and toric varieties of codimension two. After J. McCullough and I. Peeva constructed counterexamples in 2018, it has been an interesting question to find the categories such that the Eisenbud-Goto conjecture holds. So far, surface counterexamples have not been found while counterexamples of any dimension greater or equal to 3 are known. In this paper, we construct counterexamples to the Eisenbud-Goto conjecture for projective surfaces in $\mathbb{P}^4$ and investigate projective invariants, cohomological properties, and geometric properties. The counterexamples are constructed via binomial rational maps between projective spaces.
