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SUMMARY:Dharm Veer (Chennai Mathematical Institute)
DTSTART:20220325T120000Z
DTEND:20220325T130000Z
DTSTAMP:20260423T021039Z
UID:VCAS/127
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/VCAS/127/">O
 n Green-Lazarsfeld property $N_p$ for Hibi rings</a>\nby Dharm Veer (Chenn
 ai Mathematical Institute) as part of IIT Bombay Virtual Commutative Algeb
 ra Seminar\n\n\nAbstract\nLet $L$ be a finite distributive lattice. By Bir
 khoff's fundamental structure theorem\, $L$ is the ideal lattice of its su
 bposet $P$ 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 t
 hat 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 t
 he property $N_p$ of Hibi rings for $p=2$ and 3. For example\, we show tha
 t if a Hibi ring satisfies property $N_2$\, then its Segre product with a 
 polynomial ring in finitely many variables also satisfies property $N_2$.\
 n
LOCATION:https://researchseminars.org/talk/VCAS/127/
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