Lecture

Dimension of Algebraic Variety

Description

This lecture covers the concept of dimension of an algebraic variety, which is defined as the largest integer n such that there exists a chain of distinct irreducible closed subsets. The instructor explains how the dimension of an algebraic set is related to the dimension theory for rings, specifically focusing on the (Krull)-dimension of a ring. Various propositions are presented, including the relationship between the dimension of an affine algebraic variety and its coordinate ring. The lecture also discusses computing dimensions using tools from commutative algebra, such as transcendence degree and prime ideals. Additionally, the precise dimension of varieties in different scenarios, like hypersurfaces, is explored.

About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Graph Chatbot

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.