Can Apple handle a simple download ?

You can't ask for someone to share a copy because it is tied to their Apple ID and unusable for you.

Download it once and save the installer to another drive or to a flash drive before running it.

Millions of other have download Mavericks without issue.

As QuickTimeKirk says downloadable Mac OS X operating systems have been downloaded millions and millions of times.

If it is corrupt for you, it is most likely happening somewhere AFTER it leaves Apple's servers.

Since the network protocols tend to integrity check each packet, and ask for a re-transmit if an error is detected, I would strongly suspect your Mac or your disk drive as failing. It is a guess, as I suppose it could be something in the network, or since Apple uses Akamai edge servers to distribute a lot of things, maybe a bad copy in the server for your region of the world, but I would also suspect that would be corrected very quickly.

So if you have another Mac, AND/OR another location where you can download the installer, you might give that a try. If you have an Apple Store nearby, you could make a genius bar appointment to see about getting aide and assistance at the store (or at least use the Store's free WiFi - of course you may not want to drag your iMac there, unless you want to Genius Bar to analyze it for hardware problems)

Now when you install Mavericks, use a copy, so you always have the original that you can use again on another of your systems, or for a future re-install. You can even use DiskMakerX to create a bootable USB Flash Drive.