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SUMMARY:Jason McCullough (Iowa State University)
DTSTART:20210326T130000Z
DTEND:20210326T140000Z
DTSTAMP:20260423T021003Z
UID:VCAS/75
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/VCAS/75/">Th
 e Eisenbud-Goto Conjecture</a>\nby Jason McCullough (Iowa State University
 ) as part of IIT Bombay Virtual Commutative Algebra Seminar\n\n\nAbstract\
 nLet S be a polynomial ring over an algebraically closed field K.  There h
 as been considerable research into effective upper bounds for the Castelnu
 ovo-Mumford regularity of graded ideals of S.  Through the work of Bertram
 \, Ein\, Gruson\, Kwak\, Lazarsfeld\, Peskine\, and others\, there are sev
 eral good bounds for the defining ideals of smooth projective varieties in
  characteristic zero.  However\, for arbitrary ideals\, the best upper bou
 nd is doubly exponential (in terms of the number of variables and degrees 
 of generators)\, and this bound is asymptotically close to optimal due to 
 examples derived from the Mayr-Meyer construction.  In 1984\, Eisenbud and
  Goto conjectured that the regularity of a nondegenerate prime ideal P was
  at most deg(P) – codim(P) + 1\, and proved this when S/P was Cohen-Maca
 ulay (even if P is not prime).  In this talk\, I will explain the construc
 tion of counterexamples to the Eisenbud-Goto Conjecture\, joint work with 
 Irena Peeva\, through the construction of Rees-Like algebras and a special
  homogenization.  While we show that there is no linear bound on regularit
 y in terms of the degree (or multiplicity) of P\, we later showed that som
 e such bound exists.  The latter part of this talk is joint work with Giul
 io Caviglia\, Marc Chardin\, Irena Peeva\, and Matteo Varbaro.\n
LOCATION:https://researchseminars.org/talk/VCAS/75/
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