Publication

Homology of the three flag Hilbert Scheme

Daniele Boccalini
2016
Theses

Abstract

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.

Official source

https://infoscience.epfl.ch/entities/publication/09770737-a222-4d29-aa5e-a37f6099c4d8

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Daniele Boccalini
2016
Theses

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/09770737-a222-4d29-aa5e-a37f6099c4d8

About this result

Ontological neighbourhood

Mathematics

Geometry: Algebraic geometry

Related concepts (22)

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In algebraic geometry, a projective variety over an algebraically closed field k is a subset of some projective n-space over k that is the zero-locus of some finite family of homogeneous polynomials of n + 1 variables with coefficients in k, that generate a prime ideal, the defining ideal of the variety. Equivalently, an algebraic variety is projective if it can be embedded as a Zariski closed subvariety of .

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