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SUMMARY:Trung Cuong Doan (Institute of Mathematics\, Hanoi)
DTSTART:20210521T120000Z
DTEND:20210521T130000Z
DTSTAMP:20260423T021001Z
UID:VCAS/83
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/VCAS/83/">Be
 tti numbers and ideal structure of projective subschemes of almost maximal
  degree</a>\nby Trung Cuong Doan (Institute of Mathematics\, Hanoi) as par
 t of IIT Bombay Virtual Commutative Algebra Seminar\n\n\nAbstract\nSimilar
  to Castelnouvo-Mumford regularity\, reduction number is a measure of the 
 complexity of the structure of an algebra. For a projective subscheme $X$\
 , there is a degree upper bound\n$$\\deg(X)\\leq \\binom{e+r}{r}\,$$\nwher
 e $e$ is the codimension and $r$ is the reduction number of the homogeneou
 s coordinate ring. In this talk\, I discuss the maximal case $\\deg(X)=\\b
 inom{e+r}{r}$ and the almost maximal case $\\deg(X)=\\binom{e+r}{r}-1$. In
  these cases\, it is possible to explicitly describe certain initial ideal
  of the defining ideal of $X$ and consequently one obtains an explicit des
 cription of the Betti table. I also discuss how componentwise linearity is
  helpful for computing the Betti tables of projective varieties with an al
 most maximal degree.\n\nThis is a joint work with Sijong Kwak.\n
LOCATION:https://researchseminars.org/talk/VCAS/83/
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