Speaker: Dharm Veer, Chennai Mathematical Institute, India.
Date/Time: 25 March 2022, 5:30pm IST/ 12:00pm GMT / 8:00am ET (joining
time 5:15pm IST).
Gmeet link: meet.google.com/uht-oqmy-awd
Title: On Green-Lazarsfeld property $N_p$ for Hibi rings/
Abstract: Let $L$ be a finite distributive lattice. By Birkhoff's
fundamental structure theorem, $L$ is the ideal lattice of its subposet
$P$ of join-irreducible elements. Write $P=\{p_1,\ldots,p_n\}$ and let
$K[t,z_1,\ldots,z_n]$ be a polynomial ring in $n+1$ variables over a field
$K.$ The {\em Hibi ring} associated with $L$ is the subring of
$K[t,z_1,\ldots,z_n]$ generated by the monomials
$u_{\alpha}=t\prod_{p_i\in \alpha}z_i$ where $\alpha\in L$. In this talk,
we show that a Hibi ring satisfies property $N_4$ if and only if it is a
polynomial ring or it has a linear resolution. We also discuss a few
results about the property $N_p$ of Hibi rings for $p=2$ and 3. For
example, we show that if a Hibi ring satisfies property $N_2$, then its
Segre product with a polynomial ring in finitely many variables also
satisfies property $N_2$.
For more information and links to previous seminars, visit the website of
VCAS:
https://sites.google.com/view/virtual-comm-algebra-seminar