Quadratic monomial ideals with almost linear free resolutions

Abstract: This talk will be about the minimal free resolution of quadratic monomial ideals. It is well known that a quadratic monomial ideal $I$ in the polynomial ring $\mathbb{K}[x_1,\ldots, x_n]$, $\mathbb{K}$ a field, has a linear resolution if and only if $I$ is the edge ideal of the complement of a chordal graph, and this is equivalent to the linearity of the resolution of all powers of $I$.

In this talk we will discuss the case that the resolution of a quadratic monomial ideal $I$ is linear up to the homological degree $t$ with $t\geq\projdim(I)-2$, where $\projdim(I)$ denotes the projective dimension of $I$. As an outcome, we give a combinatorial classification of such ideals and also check whether their high powers have a linear resolution.

Chairperson: Siamak Yassemi, University of Tehran, Iran

Mathematics

Audience: advanced learners

IIT Bombay Virtual Commutative Algebra Seminar

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