You should not delete the hidden 'dot' files on your 'Desktop', or elsewhere; you just want to make them invisible (hidden).
Unfortunately, MacOS X is not the System / MacOS of yesterday (1984 - 2001) - and we (and others who receive compressed files from us) now must suffer from such Apple introduced annoyances as the '.DS_Store' files.
The '.DS_Store' file is Apple's, (expletives omitted) poor MacOS X implementation of folder information management. Apple has yet to incorporate the near perfect System 9.2.2 (and earlier) file management system into MacOS X; not a simple task - yet, anything would be better than the ridiculous '.DS_Store' implementation.
Other '.' files exist in each folder, and even more reside at your hard disk drive's root level (double click on your hard disk drive's icon - this is its 'root' level). These '.' files are needed for the feeble MacOS X to exist.
Once Apple learns how to, and actually implements, the System 9.2.2 and earlier file management system into MacOS X - only then perhaps, will life on a Mac be Mac like.
Ok, enough of the rant. Let us get your annoying '.' files invisible once again.
01. Copy ('Command C' or 'Edit, Copy' menu item) the next line of text ,,,
defaults write com.apple.finder AppleShowAllFiles 0; killall Finder
02. Launch 'Terminal' ('/Applications/Utilities/').
03. Do a paste ('Command V' or 'Edit, Paste' menu item).
04. Press the <return> key.
05. Quit 'Terminal'.
All once visible '.' beginning files will now be hidden.
One would think - until those at Apple fixed MacOS X'es file management system, that they would (at least) put a check box in the 'Finder's 'Preferences' 'Advance' panel titled 'Show invisible files.', to allow the user the ability to view or not all files in any 'Finder' volume or folder window. I can do such on my Windoze98 based Intel PC!
But, what does one expect from a company which merely shuffles the Preferences controls locations (of a number of its 'System Preferences' and applications) about and claims them as part of the 200+ new features of the recently selling version of MacOS X?
But then 10.4.3 is rumored to have 400+ MacOS X fixes, while 10.4.2 had its fixes, and 10.4.1 had its fixes, ...