Squarefree powers of edge ideals

Abstract: Let $G$ be a finite simple graph. The edge ideal of $G$, denoted by $I(G)$, is a monomial ideal generated by the monomials that correspond to the edges of the graph. In this talk, we will be interested in resolutions of squarefree powers of edge ideals. The $k$th squarefree power $I(G)^{[k]}$ of $I(G)$ is generated by the squarefree monomials in $I(G)^k$. We will explore the question of when squarefree powers of edge ideals are linearly related or have linear resolution. This talk is based on joint work with Jürgen Herzog, Takayuki Hibi and Sara Saeedi Madani. Chairperson - Takayuki Hibi

Mathematics

Audience: advanced learners

IIT Bombay Virtual Commutative Algebra Seminar

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