Symbolic powers of edge ideals

✍ Scribed by Carlos E.N. Bahiano

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 298 KB
• Volume: 273
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1016/s0021-8693(03)00463-0

✦ Synopsis

. . . , X n

] be an ideal in a polynomial ring over the field k. We define the essential symbolic module of I to be the R/I -module -ı) and I (m) stands for the mth symbolic power of I. We will mainly focus on the case where I is generated by square-free monomials of degree two. Among our main results are optimal bounds for the degrees of the minimal generators of F(I ), several criteria for a monomial to be such a generator and an upper bound for the generation type of the symbolic Rees algebra of I . As a byproduct we recapture the result of Simis, Vasconcelos, and Villarreal on when such an ideal is normally torsionfree.