If you say JVM, I suppose you mean Java Virtual Machine.
This has nothing to do with the kernel, Java runs under virtually any working kernel configuration.
What you need to do is install the Java (2) Runtime or Java (2) SDK package(s) delivered with your distro (names of packages may differ between - try searching for "java", "j2re", "j2sdk" etc.). Simply use your distro's package management tool. It will resolv all dependencies also, i.e. install all library-packages necessary to run Java.
If you use Debian stable, search at
www.apt-get.org to find more recent versions of Java.