Fri, April 2, 2021
Public Access

Category: All

April 2021
Mon Tue Wed Thu Fri Sat Sun
      1 2 3 4
5 6 7 8 9 10 11
12 13 14 15 16 17 18
19 20 21 22 23 24 25
26 27 28 29 30    
6:00pm [6:30pm] Jason McCullough, Iowa State University, Ames, IA, USA
Speaker: *Jason McCullough, Iowa State University, Ames, IA, USA* Date/Time: *2 April 2021, 6:30pm IST/ 1:00pm GMT / 9:00am EDT* (joining time 6:15pm IST). Google meet link: Title:* Rees-like algebras* Abstract: Given their importance in constructing counterexamples to the Eisenbud-Goto Conjecture, it is reasonable to study the algebra and geometry of Rees-like algebras further. Given a graded ideal I of a polynomial ring S, its Rees-like algebra is S[It, t^2], where t is a new variable. Unlike the Rees algebra, whose defining equations are difficult to compute in general, the Rees-like algebra has a concrete minimal generating set in terms of the generators and first syzygies of I. Moreover, the free resolution of this ideal is well understood. While it is clear that the Rees-like algebra of an ideal is never normal and only Cohen-Macaulay if the ideal is principle, I will explain that it is often seminormal, weakly normal, or F-pure. I will also discuss the computation of the singular locus, how the singular locus is affected by homogenization, and the structure of the canonical module, class group, and Picard group. This talk is joint work with Paolo Mantero and Lance E. Miller. For more information and links to previous seminars, visit the website of VCAS: