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:
https://meet.google.com/iqh-jnea-omr
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:
https://sites.google.com/view/virtual-comm-algebra-seminar