000222434 001__ 222434
000222434 005__ 20190717172528.0
000222434 0247_ $$2doi$$a10.5075/epfl-thesis-7244
000222434 02470 $$2urn$$aurn:nbn:ch:bel-epfl-thesis7244-3
000222434 02471 $$2nebis$$a10736945
000222434 037__ $$aTHESIS
000222434 041__ $$aeng
000222434 088__ $$a7244
000222434 245__ $$aHomology of the three flag Hilbert Scheme
000222434 269__ $$a2016
000222434 260__ $$bEPFL$$c2016$$aLausanne
000222434 300__ $$a131
000222434 336__ $$aTheses
000222434 502__ $$aProf. Kathryn Hess Bellwald (présidente) ; Prof. Tamás Hausel (directeur de thèse) ; Prof. Donna Testerman, Prof. Andras Szenes, Prof. Balázs Szendrói (rapporteurs)
000222434 520__ $$aWe 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.
000222434 6531_ $$aHilbert scheme
000222434 6531_ $$ahomology
000222434 6531_ $$aflags of ideals
000222434 6531_ $$aHilbert-Samuel's strata
000222434 6531_ $$aaffine paving
000222434 700__ $$0246695$$g224455$$aBoccalini, Daniele
000222434 720_2 $$aHausel, Tamás$$edir.$$g224282$$0246236
000222434 8564_ $$zn/a$$yn/a$$uhttps://infoscience.epfl.ch/record/222434/files/EPFL_TH7244.pdf$$s1993207
000222434 909C0 $$xU10122$$pGEOM$$0252345
000222434 909CO $$pthesis-bn2018$$pDOI$$pSB$$ooai:infoscience.tind.io:222434$$qDOI2$$qGLOBAL_SET$$pthesis
000222434 917Z8 $$x108898
000222434 918__ $$dEDMA$$cMATHGEOM$$aSB
000222434 919__ $$aGEOM
000222434 920__ $$b2016$$a2016-10-17
000222434 970__ $$a7244/THESES
000222434 973__ $$sPUBLISHED$$aEPFL
000222434 980__ $$aTHESIS