Jessica Sidman,
Castelnuovo-Mumford regularity basics
Over the past twenty years the fields of computational algebraic geometry
and commutative algebra have seen rapid advances due to improved
technology. One of the major reasons for studying the Castelnuovo-Mumford
regularity of a module is that it can be roughly interpreted as giving the
the module's computational complexity. I will give precise definitions, a
general idea of what kinds of results have been proved, and discuss some
of the basic methods and ideas involved in working with regularity.