Results 21 to 30 of about 405 (48)

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

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.
core   +1 more source

On Chow Stability for algebraic curves [PDF]

, 2015
In the last decades there have been introduced different concepts of stability for projective varieties. In this paper we give a natural and intrinsic criterion of the Chow, and Hilbert, stability for complex irreducible smooth projective curves $C ...
Brambila-Paz, L., Torres-Lopez, H.
core   +1 more source

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
doaj   +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
doaj   +1 more source

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
doaj   +1 more source

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

The compactified jacobian can be nonreduced

, 2015
We prove by explicit example that the compactified jacobian can be nonreduced. The example is a rational space curve of arithmetic genus 4.
Kass, Jesse Leo
core   +1 more source