**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Concept# Analytic space

Summary

An analytic space is a generalization of an analytic manifold that allows singularities. An analytic space is a space that is locally the same as an analytic variety. They are prominent in the study of several complex variables, but they also appear in other contexts.
Definition
Fix a field k with a valuation. Assume that the field is complete and not discrete with respect to this valuation. For example, this includes R and C with respect to their usual absolute values, as well as fields of Puiseux series with respect to their natural valuations.
Let U be an open subset of kn, and let f1, ..., fk be a collection of analytic functions on U. Denote by Z the common vanishing locus of f1, ..., fk, that is, let Z = { x | f1(x) = ... = fk(x) = 0 }. Z is an analytic variety.
Suppose that the structure sheaf of U is \mathcal{O}_U. Then Z has a structure sheaf \mathcal{O}_Z = \mathcal{O}_U / \mathcal{I}_Z, where \mathcal{I}_Z is the

Official source

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.

Related publications

No results

Related people

Loading

Related units

Loading

Related concepts

Loading

Related courses

Loading

Related lectures

Loading

Related people

Related units

No results

No results

Related concepts

No results

Related courses

No results

Related lectures

No results