Claudia Polini, University of Notre Dame, IN, USA
Description
Date and Time: 3 November 2020, 6:30pm IST/ 1:00pm GMT/ 09:00am EDT
(joining time: 6:15 pm IST - 6:30 pm IST)
Speaker: Claudia Polini, University of Notre Dame, IN, USA
Google meet link: meet.google.com/urk-vxwh-nri
Title: Core of ideals - Part 1
Abstract:
Let I be an ideal in a Noetherian commutative ring. Among all the closures
of I, the integral closure plays a central role. A reduction of I is a
subideal with the same integral closure. We can think of reductions as
simplifications of the given ideal, which carry most of the information
about I itself but, in general, with fewer generators. Minimal reductions,
reductions minimal with respect to inclusion, are loosely speaking the
counterpart of the integral closure. However, unlike the integral closure,
minimal reductions are not unique. For this reason we consider their
intersection, called the core of I. The core is related to adjoint and
multiplier ideals. A motivation for studying this object comes from the
Briancon-Skoda theorem. Furthermore a better understanding of the core
could lead to solving Kawamata's conjecture on the non-vanishing of
sections of certain line bundle. In this talk I will discuss the
importance of the core, its ubiquity in algebra and geometry, and some
effective formulas for its computation.