Regular Sequences and the depth function for monomial ideals

Abstract: In joint work with T\`ai Huy H\`a and Susan Morey we introduced the notion of initially regular sequences on $R/I$, where $I$ is any homogeneous ideal in a polynomial ring $R$. We will discuss this notion, and show how we can construct certain types of (initially) regular sequences on $R/I$ that give effective bounds on the depth of $R/I$. Moreover, we will discuss when these sequences remain (initially) regular sequences on $R/I^t$ and give lower bounds on $\depth R/I^t$ for $t\ge 2$.

Mathematics

Audience: advanced learners

IIT Bombay Virtual Commutative Algebra Seminar

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