I have followed the installation instructions on two machines, one with Ubuntu 18.10 and one with the newly released 19.04. Both are Intel architecture and 64bit installation.
Both the installation went ok and the desktop icon is created. However when i click the IDE icon the IDE does not start up and there is no error message.
I've ran Arduino IDE 1.8.9 on both those versions of Ubuntu so it's definitely possible.
Make sure you used the "Linux 64 bits" link from the download page, and not the "Linux ARM 64 bits" link. That has been causing some confusion lately.
If that doesn't solve the problem, start Arduino from the terminal and then post here any output that is printed. Hopefully that will give us some information about the problem.
Java has execute permission.
rob@Rob-cube1:~/Downloads/arduino-1.8.9/java/bin$ ls -g
total 940
-rwxrwxr-x 1 rob 70800 Dec 6 11:04 java
-rwxr-xr-x 1 rob 70928 Dec 6 11:04 jjs
-rwxr-xr-x 1 rob 70928 Dec 6 11:04 keytool
-rwxr-xr-x 1 rob 70952 Dec 6 11:04 orbd
-rwxr-xr-x 1 rob 70928 Dec 6 11:04 pack200
-rwxr-xr-x 1 rob 70928 Dec 6 11:04 policytool
-rwxr-xr-x 1 rob 70928 Dec 6 11:04 rmid
-rwxr-xr-x 1 rob 70928 Dec 6 11:04 rmiregistry
-rwxr-xr-x 1 rob 70928 Dec 6 11:04 servertool
-rwxr-xr-x 1 rob 70952 Dec 6 11:04 tnameserv
-rwxr-xr-x 1 rob 221872 Dec 6 11:04 unpack200
rob@Rob-cube1:~/Downloads/arduino-1.8.9/java/bin$
Picked up JAVA_TOOL_OPTIONS:
java.lang.NullPointerException
at processing.app.BaseNoGui.onBoardOrPortChange(BaseNoGui.java:679)
at processing.app.Base.onBoardOrPortChange(Base.java:1317)
at processing.app.Base$12.actionPerformed(Base.java:1544)
at processing.app.Base.rebuildBoardsMenu(Base.java:1494)
at processing.app.Base.(Base.java:275)
at processing.app.Base.main(Base.java:151)
Create a folder named portable in the Arduino IDE installation folder and then try starting it again. This puts the Arduino IDE into portable mode, which will cause it to no longer use the ~/.arduino15 folder or the usual sketchbook folder. If the IDE starts in portable mode, then we know that the problem is caused by something in the .arduino15 folder or the sketchbook folder and can proceed to troubleshoot more efficiently based on that information.