You can not do anything on your PC with an arduino but send it data on the serial port. So if you want to do anything on the PC then there must be a program running on it that receives this data, takes the appropriate action and returns information to the Arduino.
So basically no the arduino can not command this to happen directly on a PC but can command a helper program to do it. Often this program can be easily written in the language Processing which is free and multi-platform and looks very similar to the Arduino IDE, mainly because that share the same root source code.