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X-ORIGINAL-URL:https://lacim.uqam.ca
X-WR-CALDESC:Événements pour LACIM
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DTSTART:20210101T000000
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DTSTART;TZID=UTC:20210507T110000
DTEND;TZID=UTC:20210507T120000
DTSTAMP:20210509T203604
CREATED:20210222T233813Z
LAST-MODIFIED:20210506T213852Z
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SUMMARY:Patricia Klein (Université de Minnesota): Geometric vertex decomposition and liaison
DESCRIPTION:Abstract: Geometric vertex decomposition and liaison are two frameworks that have been used to produce similar results about similar families of algebraic varieties. In this talk\, we will describe an explicit connection between these approaches. In particular\, we describe how each geometrically vertex decomposable ideal is linked by a sequence of elementary G-biliaisons of height 1 to an ideal of indeterminates and\, conversely\, how every G-biliaison of a certain type gives rise to a geometric vertex decomposition. As a consequence\, we can immediately conclude that several well-known families of ideals are glicci\, including Schubert determinantal ideals\, defining ideals of varieties of complexes\, and defining ideals of graded lower bound cluster algebras. \nThis connection also gives us a framework for implementing with relative ease Gorla\, Migliore\, and Nagel’s strategy of using liaison to establish Gröbner bases. We describe briefly\, as an application of this work\, a proof of a recent conjecture of Hamaker\, Pechenik\, and Weigandt on diagonal Gröbner bases of Schubert determinantal ideals. \nThis talk is based on joint work with Jenna Rajchgot. \nAnyone who would like to attend the talk is invited to contact the organizers for the Zoom link.
URL:https://lacim.uqam.ca/event/patricia-klein-universite-de-minnesota-a-venir/
LOCATION:En ligne/online\, Canada
CATEGORIES:Séminaire du LACIM
ORGANIZER;CN="Hugh%20Thomas":MAILTO:seminar-organizers@lacim.ca
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