環面簇的纖維乘積的探討

Abstract

如何決定環面簇的纖維乘積的結構是環面幾何中一個重要但困難的問題。本文 以兩種不同的面相來探討這個問題。一種來自於基本的觀點，另一種採用組合交 換代數的技巧。對於第二種方式，我們將會研究在有相同 grading 的多項式環中 的兩個理想的纖維乘積。希望本文能夠對這個問題的研究有實質的幫助。

How to determine the toric structure of a fiber product is an important but difficult problem in toric geometry. In this article, we adopt two different approaches toward this topic. One is from the fundamental point of view and the other uses the technique in combinatorial commutative algebra. For the latter one, we study the toric fiber product of two homogeneous ideals with respect to the same multigrading. We hope this article will be helpful to further study of toric fiber products.