Abstract
We study algebras defined by finite sets G = { M 1, ..., M q } of monomials of a polynomial ring R. There are two basic algebras: (i) k[ G] = k[ M 1, ..., M q ], the k-subalgebra of R spanned by the M i , and (ii) the quotient ring R/ I( G), where I( G) = ( M 1, ..., M q ). They come together in the construction of the Rees algebra R ( I( G)) of the ideal I( G). The emphasis is almost entirely on sets of squarefree monomials of degree two and their attached graphs. The main results are assertions about the Cohen-Macaulay behaviour of the Koszul homology of I( G), and how normality or Cohen-Macaulayness of one of the algebras can be read off the properties of the graph or in the other algebra.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
