Auditing file deletions

Yes you can.
(source MSW2K help)
You can audit the access of files and folders on NTFS volumes to identify who took various types of actions with the files and folders.

When you audit a file or folder, an entry is written to the Event Viewer security log whenever the file or folder is accessed in a certain way. You specify which files and folders to audit, whose actions to audit, and what types of actions are audited.

To set auditing on a file or folder, use Group Policy to enable auditing, and then use Windows Explorer to specify which files to audit and which type of file access events to audit.

You can audit successful and failed attempts of the following types of folder and file access:

Types of folder access Types of file access

Displaying names of files in the folder Displaying the file's data
Displaying folder attributes Displaying file attributes
Changing folder attributes Displaying the file's owner and permissions
Creating subdirectories and files Changing the file
Going to the folder's subdirectories Changing file attributes
Displaying the folder's owner and permissions Running the file
Deleting the folder Deleting the file
Changing folder permissions Changing the file's permissions
Changing folder ownership Changing the file's ownership

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