222434
20190717172528.0
doi
10.5075/epfl-thesis-7244
urn
urn:nbn:ch:bel-epfl-thesis7244-3
nebis
10736945
THESIS
eng
7244
Homology of the three flag Hilbert Scheme
Lausanne
EPFL
2016
2016
131
Theses
Prof. Kathryn Hess Bellwald (présidente) ; Prof. Tamás Hausel (directeur de thèse) ; Prof. Donna Testerman, Prof. Andras Szenes, Prof. Balázs Szendrói (rapporteurs)
We prove the existence of an affine paving for the three-step flag Hilbert scheme that parametrizes flag of three 0-dimensional subschemes of length, respectively, n, n+1 and n+2 that are supported at the origin of the affine plane. This is done by showing that the space stratifies in smooth subvarieties, the Hilbert-Samuel's strata, each of which has an affine paving with cells of known dimension, indexed by marked Young diagrams. The affine pavings of the Hilbert-Samuel's strata allow us to prove that the Poincaré polynomials for our spaces satisfy a generating function. In the process of proving the formula for the generating function we relate combinatorially the homology of our spaces with that of known smooth subspaces of another Hilbert scheme of flags, this time of length n and n+2. As a corollary we find an affine paving and a combinatorial formula for the Poincaré of these last ambient spaces.
Hilbert scheme
homology
flags of ideals
Hilbert-Samuel's strata
affine paving
246695
Boccalini, Daniele
224455
246236
Hausel, Tamás
dir.
224282
1993207
http://infoscience.epfl.ch/record/222434/files/EPFL_TH7244.pdf
n/a
n/a
252345
GEOM
U10122
oai:infoscience.tind.io:222434
SB
DOI
thesis-bn2018
thesis
GLOBAL_SET
DOI2
108898
SB
MATHGEOM
EDMA
GEOM
2016-10-17
2016
7244/THESES
EPFL
PUBLISHED
THESIS