Results 21 to 30 of about 406 (47)

The integral cohomology of the Hilbert scheme of points on a surface

Forum of Mathematics, Sigma, 2020
We show that if X is a smooth complex projective surface with torsion-free cohomology, then the Hilbert scheme $X^{[n]}$ has torsion-free cohomology for every natural number n.
Burt Totaro
doaj   +1 more source

Gotzmann's persistence theorem for finite modules [PDF]

, 2015
We prove a generalization of Gotzmann's persistence theorem in the case of modules with constant Hilbert polynomial. As a consequence, we show that the defining equations that give the embedding of a Quot scheme of points into a Grassmannian are given by
Ståhl, Gustav Sædén
core   +1 more source

The Hilbert scheme of hyperelliptic Jacobians and moduli of Picard sheaves

, 2020
Let $C$ be a hyperelliptic curve embedded in its Jacobian $J$ via an Abel-Jacobi map. We compute the scheme structure of the Hilbert scheme component of $\textrm{Hilb}_J$ containing the Abel-Jacobi curve as a point.
Ricolfi, Andrea T.
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DONALDSON–THOMAS INVARIANTS OF LOCAL ELLIPTIC SURFACES VIA THE TOPOLOGICAL VERTEX

Forum of Mathematics, Sigma, 2019
We compute the Donaldson–Thomas invariants of a local elliptic surface with section. We introduce a new computational technique which is a mixture of motivic and toric methods. This allows us to write the partition function for the invariants in terms of
JIM BRYAN, MARTIJN KOOL
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Cones of Hilbert functions [PDF]

, 2014
We study the closed convex hull of various collections of Hilbert functions. Working over a standard graded polynomial ring with modules that are generated in degree zero, we describe the supporting hyperplanes and extreme rays for the cones generated by
G. Smith, Gregory, Mats Boij
core   +1 more source

Transverse Hilbert schemes and completely integrable systems

Complex Manifolds, 2017
In this paper we consider a special class of completely integrable systems that arise as transverse Hilbert schemes of d points of a complex symplectic surface S projecting onto ℂ via a surjective map p which is a submersion outside a discrete subset of ...
Donin Niccolò Lora Lamia
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THE MOTIVE OF THE HILBERT CUBE $X^{[3]}$

Forum of Mathematics, Sigma, 2016
The Hilbert scheme $X^{[3]}$ of length-3 subschemes of a smooth projective variety $X$
MINGMIN SHEN, CHARLES VIAL
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Non-effective Deformations of Grothendieck's Hilbert Functor

, 2006
Let X be a scheme that does not satisfy the valuative criterion of separatedness. We show that the Hilbert functor parametrizing closed families of X that are flat, finite and of rank one is not represented by a scheme or an algebraic space.Comment: 8 ...
Lundkvist, Christian, Skjelnes, Roy
core   +3 more sources

THE INTEGRAL COHOMOLOGY OF THE HILBERT SCHEME OF TWO POINTS

Forum of Mathematics, Sigma, 2016
The Hilbert scheme $X^{[a]}$ of points on a complex manifold $X$
BURT TOTARO
doaj   +1 more source

On singular Hilbert schemes of points: Local structures and tautological sheaves [PDF]

Épijournal de Géométrie Algébrique
We show an intrinsic version of Thomason's fixed-point theorem. Then we determine the local structure of the Hilbert scheme of at most $7$ points in $\mathbb{A}^3$. In particular, we show that in these cases, the points with the same extra dimension have
Xiaowen Hu
doaj   +1 more source