**Date & Time:** 20th April, 2012, 15:30-17:00.

**Venue:** Ramanujan Hall

**Title:**Zariski's Theory of complete ideals

**Speaker: ** J.K.Verma, IIT Bombay

**Abstract:** We will finish the proof of the Lipman-Rees Theorem about their
numerical characterisation of contracted ideals. We will then introduce
the characteristic form of an m-primary ideal in a two dimensional RLR.
This gives an explicit characterisation of quadratic transforms from which
an ideal may be contracted. We shall also prove that a complete ideal
is contracted from some quadratic transform which is a major step in
the preparation of Zariski's theorem, viz: product of complete ideals
is complete in a two dimensional RLR.