If we are subscribed to alert on any SharePoint list or library, we get email notifications along with link to the list or library.
Lets assume the following scenario
| Internal Web Application URL | http://sp-realm/ |
| Public web application URL | https://access.sharepointrealm.com |
| Document Library | Results |
| Internal URL of Document Library | http://sp-realm/Results |
When we create an alert for this library, we get email with the internal link to this document library by default.
If we want to associate public URL with this library, all we have to do is change Alternate Access Mapping and provide public URL in place of Default Zone for that particular web application.
Good Luck !
