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SUMMARY:Juergen Herzog (University of Duisberg-Essen)
DTSTART:20210108T120000Z
DTEND:20210108T130000Z
DTSTAMP:20260423T021010Z
UID:VCAS/64
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/VCAS/64/">Po
 wers of component wise linear ideals</a>\nby Juergen Herzog (University of
  Duisberg-Essen) as part of IIT Bombay Virtual Commutative Algebra Seminar
 \n\n\nAbstract\nLet $S=K[x_1\,\\ldots\,x_n]$ be the polynomial ring over a
  field and   $A$ a standard graded  $S$-algebra. In terms of the Groebner 
 basis of the defining ideal $J$ of $A$ we give a condition\, called the x-
 condition\, which implies that all graded components $A_k$  of $A$ have li
 near quotients and with additional assumptions are componentwise linear. A
  typical example of such an algebra is the Rees ring $\\mathcal R(I)$ of a
  graded ideal or the symmetric algebra $\\text{Sym}(M)$ of a module $M$. W
 e apply our criterion to study certain symmetric algebras and the powers o
 f vertex cover ideals of certain classes of graphs. This is a report on jo
 int work with Takayuki Hibi and Somayeh Moradi.\n
LOCATION:https://researchseminars.org/talk/VCAS/64/
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