TL;DR

Add the Xdg.Directories package to your project:

dotnet add package Xdg.Directories

Then use the BaseDirectory and UserDirectory classes to access the XDG directories:

using System;
using System.IO;
using Xdg.Directories;

// Prints /home/$USER/.local/share
Console.Writeline(BaseDirectory.DataHome);

// Prints /home/$USER/Documents
Console.Writeline(UserDirectory.DocumentsDir);

// Create and open a new cache file under the "foo" directory
FileStream file = File.Open(BaseDirectory.CacheFile("foo/bar.json"), FileMode.OpenOrCreate);

For more information, see the API documentation.

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TL;DR