BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jason McCullough (Iowa State University) DTSTART:20210402T130000Z DTEND:20210402T140000Z DTSTAMP:20260423T021002Z UID:VCAS/74 DESCRIPTION:Title: Re es-like Algebras\nby Jason McCullough (Iowa State University) as part of IIT Bombay Virtual Commutative Algebra Seminar\n\n\nAbstract\nGiven the ir importance in constructing counterexamples to the Eisenbud-Goto Conject ure\, it is reasonable to study the algebra and geometry of Rees-like alge bras further. Given a graded ideal I of a polynomial ring S\, its Rees-li ke algebra is S[It\, t^2]\, where t is a new variable. Unlike the Rees al gebra\, whose defining equations are difficult to compute in general\, the Rees-like algebra has a concrete minimal generating set in terms of the g enerators and first syzygies of I. Moreover\, the free resolution of this ideal is well understood. While it is clear that the Rees-like algebra o f an ideal is never normal and only Cohen-Macaulay if the ideal is princip al\, I will explain that it is often seminormal\, weakly normal\, or F-pur e. I will also discuss the computation of the singular locus\, how the si ngular locus is affected by homogenization\, and the structure of the cano nical module\, class group\, and Picard group. This talk is joint work wi th Paolo Mantero and Lance E. Miller.\n LOCATION:https://researchseminars.org/talk/VCAS/74/ END:VEVENT END:VCALENDAR