Very strange situation.
Yes compiz-core-abiversion-20151010 is virtual on xenial and zesty, but it is provided by compiz-core:
$ apt-cache show compiz-core | grep "Version\|Provides\|Package"
Package: compiz-core
Version: 1:0.9.12.3+16.04.20180221-0ubuntu1
Provides: compiz-core-abiversion-20180221
Package: compiz-core
Version: 1:0.9.12.2+16.04.20160415-0ubuntu1
Provides: compiz-core-abiversion-20151010
So APT and dpkg knows about both of them.
Full list of compiz-core-abiversion family is as follows:
$ aptitude search compiz-core-abiversion-
v compiz-core-abiversion-20151010 -
v compiz-core-abiversion-20151010:i386 -
v compiz-core-abiversion-20180221 -
v compiz-core-abiversion-20180221:i386 -
Here as we know compiz-core-abiversion-20151010 is not installable:
$ sudo apt-get install compiz-core-abiversion-20151010
Reading package lists... Done
Building dependency tree
Reading state information... Done
Package compiz-core-abiversion-20151010 is a virtual package provided by:
compiz-core 1:0.9.12.2+16.04.20160415-0ubuntu1 [Not candidate version]
E: Package 'compiz-core-abiversion-20151010' has no installation candidate
But we can install newer (actual) version:
$ sudo apt-get install compiz-core-abiversion-20180221
Reading package lists... Done
Building dependency tree
Reading state information... Done
Note, selecting 'compiz-core' instead of 'compiz-core-abiversion-20180221'
The following additional packages will be installed:
compiz-gnome compiz-plugins compiz-plugins-default libcompizconfig0 libdecoration0 libunity-core-6.0-9 unity unity-schemas unity-services
The following packages will be upgraded:
compiz-core compiz-gnome compiz-plugins compiz-plugins-default libcompizconfig0 libdecoration0 libunity-core-6.0-9 unity unity-schemas
unity-services
10 upgraded, 0 newly installed, 0 to remove and 32 not upgraded.
Need to get 5 302 kB of archives.
After this operation, 278 kB of additional disk space will be used.
Do you want to continue? [Y/n] n
So on normal consistent system all we need is to have all upgrades installed.
But if unity package was removed, we can install it with:
sudo aptitude update
sudo aptitude safe-upgrade
sudo aptitude install unity ubuntu-desktop
Note 1: My Ubuntu 16.04 LTS installations with Unity and MATE DE (1 clean xenial and and 3 old precise->trusty->xenial) work normally after regular upgrades without my intervention. All these systems did not tried to remove neither Unity nor ubuntu-desktop during upgrades. And of course xenial-proposed is disabled on my system, since I do not want to transform my Ubuntu LTS to bleeding-edge self-breakable ArchLinux.
Note 2: I edited my answer 2018-03-12 because of the fact that compiz-core-abiversion-20170630 was removed from repositories.
Best Answer
As you have found, the edgers PPA can be very unstable - it is frequently updated. Some updates are OK - some will break your system.
My general advice would be - if you find that a particular update from edgers work for you, then untick the box in software sources for the edgers PPA, so no further updates are received which can break your system.
I note that you are using both the edgers PPA and Kernel 2.6.39-3. Can I ask why?
You perhaps can either wait for a few days to see if a further update to edgers works - or you can ppa_purge the edgers PPA to return to a known Natty build configuration.
If you want to do a ppa_purge, then in a terminal:
You may have to also boot from the standard Natty kernel, 2.6.38.x