Description

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

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

Date

Fri, March 25, 2022

Start Time

5:30pm IST

Priority

5-Medium

Access

Public

Created by

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Updated

Fri, March 25, 2022 10:39am IST