Zero-Dimensional Gorenstein Ideals in Two Variables
Date Issued
2014
Date
2014
Author(s)
Wang, Yi-Shan
Abstract
In this thesis, we are interested in zero-dimensional Gorenstein ideals of the form ((xn,yn) : Fk) where Fk is a homogeneous polynomial of degree k in K[x,y], K an algebraically closed field. Firstly, we figure out the necessary and sufficient condition for a homogenous polynomial to be in ((xn,yn) : Fk) where k ≤ n and the coefficient of xk, denoted by c0, is nonzero. Next, we declare that in this case ((xn,yn) : Fk) can be generated by two elements. Then expand the result to ar- bitrary c0 and k. At last, we introduce some lemmas from the work of Genoway, Ortiz-Albino, and Tavares [8] along with revised proofs and an example in 3 vari- ables.
Subjects
Gorenstein 理想
生成元
Type
thesis
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