10,693 research outputs found
Chern Classes of Tautological Sheaves on Hilbert Schemes
We give an algorithmic description of the action of the Chern classes of
tautological bundles on the cohomology of Hilbert schemes of points on surfaces
within the framework of Nakajima's oscillator algebra. This leads to an
identification of the cohomology ring of Hilbert schemes of the affine plane
with a ring of differential operators on a Fock space. We end with the
computation of the top Segre classes of tautological bundles associated to line
bundles on Hilb^n up to n=7, and give a conjecture for the generating series.Comment: 45 pages, LaTe
Vulnerability analysis of three remote voting methods
This article analyses three methods of remote voting in an uncontrolled
environment: postal voting, internet voting and hybrid voting. It breaks down
the voting process into different stages and compares their vulnerabilities
considering criteria that must be respected in any democratic vote:
confidentiality, anonymity, transparency, vote unicity and authenticity.
Whether for safety or reliability, each vulnerability is quantified by three
parameters: size, visibility and difficulty to achieve. The study concludes
that the automatisation of treatments combined with the dematerialisation of
the objects used during an election tends to substitute visible vulnerabilities
of a lesser magnitude by invisible and widespread vulnerabilities.Comment: 15 page
Invariant deformation theory of affine schemes with reductive group action
We develop an invariant deformation theory, in a form accessible to practice,
for affine schemes equipped with an action of a reductive algebraic group
. Given the defining equations of a -invariant subscheme ,
we device an algorithm to compute the universal deformation of in terms of
generators and relations up to a given order. In many situations, our algorithm
even computes an algebraization of the universal deformation. As an
application, we determine new families of examples of the invariant Hilbert
scheme of Alexeev and Brion, where is a classical group acting on a
classical representation, and describe their singularities.Comment: 43 pages, final version, to appear in J. Pure Appl. Algebr
On the symplectic eightfold associated to a Pfaffian cubic fourfold
We show that the irreducible holomorphic symplectic eightfold Z associated to
a cubic fourfold Y not containing a plane is deformation-equivalent to the
Hilbert scheme of four points on a K3 surface. We do this by constructing for a
generic Pfaffian cubic Y a birational map Z ---> Hilb^4(X), where X is the K3
surface associated to Y by Beauville and Donagi. We interpret Z as a moduli
space of complexes on X and observe that at some point of Z, hence on a Zariski
open subset, the complex is just the ideal sheaf of four points.Comment: 9 pages. Minor changes; to appear in Crelle as an appendix to
1305.017
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