Tiny scratches on the windshield, plz help
 

Fist of all, I can't get pictures of the scratches because they are on the glass and my camera is just not that good.

My car was parked in Brooklyn last weekend when this occured. I found a cigarette that was put out (not sure if this is what caused the scratches) resting on my hood.

When I was driving back home the sun was reflecting off of the scratches. From the driver seat it looked like the thread from a spider.

When I got home I took a closer look. There is a clump of scratches in the window and the scratches appear to be caused by a bunch of circular motions, similar to that of someone putting out a smoke.

My question is, How can I get rid of these scratches?
Might they just "buff out?"

Thank you for your suggestions and time.

I would try buffing the glass with some polish and or compound and see if you can smooth them out