scholarly journals Hilbert scheme of twisted cubics as a simple wall-crossing

2018 ◽  
Vol 370 (8) ◽  
pp. 5535-5559
Author(s):  
Bingyu Xia
Keyword(s):  
Hilbert Scheme ◽  
Wall Crossing ◽  
Twisted Cubics

scholarly journals Cohomology of quiver moduli, functional equations, and integrality of Donaldson–Thomas type invariants

2011 ◽  
Vol 147 (3) ◽  
pp. 943-964 ◽  
Author(s):  
Markus Reineke
Keyword(s):  
Moduli Spaces ◽  
Hilbert Scheme ◽  
Functional Equations ◽  
Euler Characteristics ◽  
System Of Functional Equations ◽  
Representations Of Quivers ◽  
Wall Crossing

AbstractA system of functional equations relating the Euler characteristics of moduli spaces of stable representations of quivers and the Euler characteristics of (Hilbert-scheme-type) framed versions of quiver moduli is derived. This is applied to wall-crossing formulas for the Donaldson–Thomas type invariants of M. Kontsevich and Y. Soibelman, in particular confirming their integrality.

scholarly journals The space of twisted cubics

2021 ◽  
Vol Volume 5 ◽  
Author(s):  
Katharina Heinrich ◽  
Roy Skjelnes ◽  
Jan Stevens
Keyword(s):  
Hilbert Scheme ◽  
Hilbert Polynomial ◽  
Final Version ◽  
Twisted Cubic ◽  
Twisted Cubics

We consider the Cohen-Macaulay compactification of the space of twisted cubics in projective n-space. This compactification is the fine moduli scheme representing the functor of CM-curves with Hilbert polynomial 3t+1. We show that the moduli scheme of CM-curves in projective 3-space is isomorphic to the twisted cubic component of the Hilbert scheme. We also describe the compactification for twisted cubics in n-space. Comment: 22 pages. Final version

scholarly journals On the Hilbert Scheme Compactification of the Space of Twisted Cubics

1985 ◽  
Vol 107 (4) ◽  
pp. 761 ◽  
Author(s):  
Ragni Piene ◽  
Michael Schlessinger
Keyword(s):  
Hilbert Scheme ◽  
Twisted Cubics

scholarly journals Wall-crossing invariants: from quantum mechanics to knots

2015 ◽  
Vol 120 (3) ◽  
pp. 549-577 ◽  
Author(s):  
D. Galakhov ◽  
A. Mironov ◽  
A. Morozov
Keyword(s):  
Quantum Mechanics ◽  
Wall Crossing

scholarly journals Transverse Hilbert schemes and completely integrable systems

2017 ◽  
Vol 4 (1) ◽  
pp. 263-272 ◽  
Author(s):  
Niccolò Lora Lamia Donin
Keyword(s):  
Integrable Systems ◽  
Hilbert Scheme ◽  
Symplectic Form ◽  
Initial Surface ◽  
Hilbert Schemes ◽  
Completely Integrable Systems ◽  
Completely Integrable ◽  
Symplectic Surface ◽  
Complex Symplectic ◽  
Minimum Polynomial

Abstract 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 S. We explicitly endow the transverse Hilbert scheme Sp[d] with a symplectic form and an endomorphism A of its tangent space with 2-dimensional eigenspaces and such that its characteristic polynomial is the square of its minimum polynomial and show it has the maximal number of commuting Hamiltonians.We then provide the inverse construction, starting from a 2ddimensional holomorphic integrable system W which has an endomorphism A: TW → TW satisfying the above properties and recover our initial surface S with W ≌ Sp[d].

scholarly journals No more walls! A tale of modularity, symmetry, and wall crossing for 1/4 BPS dyons

2017 ◽  
Vol 2017 (5) ◽  
Author(s):  
Natalie M. Paquette ◽  
Roberto Volpato ◽  
Max Zimet
Keyword(s):  
Wall Crossing

scholarly journals MATRIX THEORY, HILBERT SCHEME AND INTEGRABLE SYSTEM

1998 ◽  
Vol 13 (34) ◽  
pp. 2731-2742 ◽  
Author(s):  
YUTAKA MATSUO
Keyword(s):  
Hilbert Scheme ◽  
Matrix Theory ◽  
Fock Space ◽  
Homology Class ◽  
Orthogonal Basis ◽  
Inner Product ◽  
Virasoro Symmetry ◽  
Hilbert Scheme Of Points ◽  
The Matrix ◽  
Boson Fock Space

We give a reinterpretation of the matrix theory discussed by Moore, Nekrasov and Shatashivili (MNS) in terms of the second quantized operators which describes the homology class of the Hilbert scheme of points on surfaces. It naturally relates the contribution from each pole to the inner product of orthogonal basis of free boson Fock space. These bases can be related to the eigenfunctions of Calogero–Sutherland (CS) equation and the deformation parameter of MNS is identified with coupling of CS system. We discuss the structure of Virasoro symmetry in this model.

scholarly journals Double-generic initial ideal and Hilbert scheme

2016 ◽  
Vol 196 (1) ◽  
pp. 19-41 ◽  
Author(s):  
Cristina Bertone ◽  
Francesca Cioffi ◽  
Margherita Roggero
Keyword(s):  
Hilbert Scheme ◽  
Initial Ideal ◽  
Generic Initial Ideal

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

2020 ◽  
Vol 8 ◽  
Author(s):  
Burt Totaro
Keyword(s):  
Natural Number ◽  
Hilbert Scheme ◽  
Obstruction Theory ◽  
Projective Surface ◽  
Hilbert Schemes ◽  
Complex Projective Surface ◽  
Smooth Complex ◽  
Hilbert Scheme Of Points ◽  
Complex Projective ◽  
Torsion Free

Abstract 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. This extends earlier work by Markman on the case of Poisson surfaces. The proof uses Gholampour-Thomas’s reduced obstruction theory for nested Hilbert schemes of surfaces.

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