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SUMMARY:Alessio Sammartano (Politecnico di Milano)
DTSTART:20220408T120000Z
DTEND:20220408T130000Z
DTSTAMP:20260423T021044Z
UID:VCAS/129
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/VCAS/129/">N
 ested Hilbert schemes of the plane</a>\nby Alessio Sammartano (Politecnico
  di Milano) as part of IIT Bombay Virtual Commutative Algebra Seminar\n\n\
 nAbstract\nThe Hilbert scheme of points Hilb^n(A^2)\, parametrizing finite
  subschemes of the plane of degree n\, is a well studied and well behaved 
 parameter space. A classical theorem of Fogarty states that it is a smooth
  variety of dimension 2n. By contrast\, the nested Hilbert scheme Hilb^(n_
 1\,n_2)(A^2)\, parametrizing nested pairs of subschemes of degrees n_1 and
  n_2\, are usually singular\, and very little is known about their singula
 rities. Using techniques from commutative algebra\, we prove that the nest
 ed Hilbert scheme Hilb^(n\,2)(A^2) has rational singularities. This is a j
 oint work with Ritvik Ramkumar.\n
LOCATION:https://researchseminars.org/talk/VCAS/129/
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