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SUMMARY:Claudia Polini (University of Notre Dame)
DTSTART:20201103T130000Z
DTEND:20201103T140000Z
DTSTAMP:20260423T021014Z
UID:VCAS/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/VCAS/5/">The
  core of ideals</a>\nby Claudia Polini (University of Notre Dame) as part 
 of IIT Bombay Virtual Commutative Algebra Seminar\n\n\nAbstract\nLet I be 
 an ideal in a Noetherian commutative ring. Among all the closures\nof I\, 
 the integral closure plays a central role. A reduction of I\nis a sub idea
 l with the same integral closure.\nWe can think of reductions as simplific
 ations of the given ideal\,\nwhich carry most of the information about I i
 tself but\, in general\,\nwith fewer generators. Minimal reductions\, redu
 ctions\nminimal with respect to inclusion\, are loosely speaking the\ncoun
 terpart of the integral closure.  However\,\nunlike the integral closure\,
  minimal reductions are not unique.\nFor this reason\, we consider their i
 ntersection\, called the core of\nI. The core is  related to adjoint and\n
 multiplier ideals. Motivation for studying\nthis object comes from the Bri
 ancon-Skoda theorem. Furthermore\,\na better understanding of the core cou
 ld lead\nto solving Kawamata's conjecture on the non-vanishing of\nsection
 s of a certain line bundle. In this talk\, I will discuss the\nimportance 
 of the core\, its ubiquity in algebra and geometry\,\nand some effective f
 ormulas for its computation.\n
LOCATION:https://researchseminars.org/talk/VCAS/5/
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