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Commutative Algebra Webinar وبینار جبر جابجایی




TITLE  
Minimal free resolution of circuit ideal of chordal clutters


LECTURER  
Ali Akbar Yazdan Pour  
Institute for Advanced Studies in Basic Sciences, Zanjan, Iran  
 


TIME  
Thursday, November 12, 2020,   11:00 - 13:00


VENUE   Online



SUMMARY

 

Minimal free resolution of monomial ideals is one of the central topics in combinatorial commutative algebra. Many of numerical invariants of an ideal are encoded in Betti numbers obtained from minimal free resolution. In general, adding a generator $u$ to a given ideal $I$ may cause changing almost all Betti numbers of the new ideal $I+(u)$. In this talk, we consider a square-free monomial ideal $I$ and we show that under some conditions on a square-free monomial $u$, the Betti numbers of $I+(u)$ can be computed by those of $I$. Based on this result, for a given clutter $\mathcal{C}$, we define the concept of simplicial sublutters and we show that the Betti numbers of the associated ideal of simplicial subclutters can be computed in terms of those of $\mathcal{C}$. We will show that for any ideal $I$ with linear resolution, there exists a simplicial subclutter $\mathcal{C}$ of complete clutter such that both of $I$ and and $I(\bar{\mathcal{C}})$ share the same Betti numbers. Chordal clutters as introduced in \cite{BYZ} are class of clutters such that $\varnothing$ is a simplicial subclutter. It is shown that the corresponding ideal of a chordal clutter has a linear resolution over all fields. For such ideals, we compute explicitly the minimal free resolution of the corresponding ideal.
This talk is based on joint work with M. Bigdeli.
To join the meeting, go to the following link: https://vmeeting.ipm.ir/b/mat-9px-g3c

 




تهران، ضلع‌ جنوبی ميدان شهيد باهنر (نياوران)، پژوهشگاه دانش‌های بنيادی، پژوهشکده رياضيات
School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Niavaran Bldg., Niavaran Square, Tehran
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