论文标题
正常的二维奇异性中的正常希尔伯特系数和椭圆形的理想
Normal Hilbert coefficients and elliptic ideals in normal two-dimensional singularities
论文作者
论文摘要
令$（a，\ mathfrak m）$为极好的二维普通本地域。在本文中，我们根据Wagreich和Yau给出的定义，研究了$ a $的椭圆形和强烈的椭圆形理想，目的是表征椭圆形和强烈的椭圆形奇点。与理性的概念类似，从主要的结果中，我们根据$ a $ a $的正常$ \ mathfrak m $ $ $ $ $ $ $ $ $ $ MATHFRAK M $ $ $ $ $的理想来表征强烈的椭圆形奇异性。与$ p_g $ - 理想不同，椭圆理想和强烈的椭圆形理想不一定是正常的，必要的和足够的条件。在最后一部分中，我们讨论了在任何二维正常局部环中强烈椭圆形理想的存在（以及有效的结构）。
Let $(A,\mathfrak m)$ be an excellent two-dimensional normal local domain. In this paper we study the elliptic and the strongly elliptic ideals of $A$ with the aim to characterize elliptic and strongly elliptic singularities, according to the definitions given by Wagreich and by Yau. In analogy with the rational singularities, in the main result we characterize a strongly elliptic singularity in terms of the normal Hilbert coefficients of the integrally closed $\mathfrak m$-primary ideals of $A$. Unlike $p_g$-ideals, elliptic ideals and strongly elliptic ideals are not necessarily normal and necessary and sufficient conditions for being normal are given. In the last section we discuss the existence (and the effective construction) of strongly elliptic ideals in any two-dimensional normal local ring.
