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SUMMARY:Marked bases and Hilbert schemes of points - Paolo Lella (Politecn
 ico di Milano)
DTSTART:20240122T100000Z
DTEND:20240122T110000Z
UID:TALK208048@talks.cam.ac.uk
DESCRIPTION:Marked bases are special sets of generators of polynomial idea
 ls. I will begin by comparing marked bases with other type of generators (
 Gr&ouml\;bner/border bases) focusing on computational aspects and on the s
 tudy of deformations of ideals.\nIn the second part of the talk\, I will e
 xplain how to use marked bases for studying the Hilbert scheme of points. 
 In particular\, I will discuss the construction of counterexamples to the 
 so-called &ldquo\;Parity conjecure&rdquo\; which states that the dimension
  of the tangent space to the Hilbert scheme of d points in the affine 3-sp
 ace has (at any point) the same parity of d.\nThe construction of the coun
 terexamples is a joint result with Luca Giovenzana\, Franco Giovenzana and
  Michele Graffeo.
LOCATION:Seminar Room 1\, Newton Institute
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