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SUMMARY:Selvi Kara (University of South Alabama)
DTSTART:20210617T163000Z
DTEND:20210617T173000Z
DTSTAMP:20260422T054627Z
UID:SFUQNTAG/35
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SFUQNTAG/35/
 ">Blow-Up Algebras of Strongly Stable Ideals</a>\nby Selvi Kara (Universit
 y of South Alabama) as part of SFU NT-AG seminar\n\n\nAbstract\nLet $S$ be
  a polynomial ring and $I_1\,\\ldots\, I_r$ be a collection of ideals in $
 S$. The multi-Rees algebra $\\mathcal{R} (I_1\,\\ldots\, I_r)$ of this col
 lection of ideals encode many algebraic properties of these ideals\, their
  products\, and powers. Additionally\, the multi-Rees algebra  $\\mathcal{
 R} (I_1\,\\ldots\, I_r)$ arise in successive blowing up of $\\textrm{Spec 
 } S$ at the subschemes defined by $I_1\,\\ldots\, I_r$. Due to this connec
 tion\, Rees and multi-Rees algebras are also called blow-up algebras in th
 e literature.\n\nIn this talk\, we will focus on Rees and multi-Rees algeb
 ras of strongly stable ideals. In particular\, we will discuss the Koszuln
 ess of these algebras through a systematic study of these objects via thre
 e parameters: the number of ideals in the collection\, the number of Borel
  generators of each ideal\, and the degrees of Borel generators. In our st
 udy\, we utilize combinatorial objects such as fiber graphs to detect Grö
 bner bases and Koszulness of these algebras. This talk is based on a joint
  work with Kuei-Nuan Lin and Gabriel Sosa.\n
LOCATION:https://researchseminars.org/talk/SFUQNTAG/35/
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