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Showing 1 to 17 of 17 for “"Hilbert Scheme"”.
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Relative Hilbert scheme methods in pseudoholomorphic geometry
… which counts holomorphic sections of a relative Hilbert scheme constructed from a symplectic Lefschetz fibration, and a number of considerations, including a duality relation for DS proven by Smith, led to the conjecture that DS agrees with the Gromov invariant G[gamma] earlier defined by C. …
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On the super Hilbert scheme of constant Hilbert polynomials
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2017-09-29 without embargo terms
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Quantum cohomology of a Hilbert scheme of a Hirzebruch surface
… we first use the ${\mathbb C^*}^2$-action on the Hilbert scheme of two points on a Hirzebruch surface to compute all one-pointed and some two-pointed Gromov-Witten invariants via virtual localization, then making intensive use of the associativity law satisfied by quantum product, calculate other …
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Deformations of the Hilbert scheme of points on a del Pezzo surface
The Hilbert scheme of $n$ points in a smooth del Pezzo surface $S$ parameterizes zero-dimensional subschemes with length $n$ on $S$. We construct a flat family of deformations of Hilb$^n S$ which can be conceptually understood as the family of Hilbert schemes of points on a family of noncommutative …
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Geometric Invariant Theory Quotient of the Hilbert Scheme of Six Points on the Projective Plane
… provide an asymptotic stability portrait for the Hilbert scheme of six points on the complex projective plane, and provide a description of its geometric invariant theory (GIT) quotient.
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Lines on Fano hypersurfaces
In this thesis, the Hilbert scheme of lines on smooth hypersurfaces is studied. The main result is that the Hilbert scheme of lines on any smooth Fano hypersurface of degree d =/< 6 in ... has the expected dimension 2n - d - 3, if k is an algebraically closed field of characteristic zero.
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A compact moduli space for Cohen-Macaulay curves in projective space
… comes from trying to interpolate between the Hilbert scheme and the Kontsevich mapping space. The main result of this thesis is that our functor is represented by a proper algebraic space. As an application we obtain interesting compactifications of the spaces of smooth curves in projective …
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Hyper-Kaehler fibrations and Hilbert schemes
… manifold is deformation equivalent to a Hilbert scheme of two points on a K3 surface.
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Surface multi-space
… variables. The main technical tool is the Hilbert scheme of points on a surface, which we adapt to the context of smooth manifolds. We begin the study of prolongations of group actions, their invariants, and the process of extending a differential equation to multi-space, whereby the …
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The logarithmic Quot space
… Quot space which generalises the Quot schemes of a variety X to the geometry of a pair (X,D) with D a simple normal crossing divisor on X. Such logarithmic Quot spaces interact well with degeneration and gluing formulae. We prove that the logarithmic Quot space is a separated and …
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Aspects of the (0,2)-McKay Correspondence
… when the resolution used is the </p><p>G-Hilbert scheme, and note that this lower bound can be found using a combinatorial count of (0,2)-deformation moduli fields for</p><p>N=(2,2) conformal field theories on the orbifold. We also find that in general this minimum is not achieved, and …
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Counting coloured boxes
… partition functions of the orbifold and its G-Hilbert scheme resolution. We formulate a crepant resolution conjecture for the Donaldson-Thomas theory of local orbifolds satisfying the Hard Lefschetz condition.
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Finite dimensional representations of sympletic reflection algebras for wreath products
… such as symplectic quotient singularities, Hilbert scheme of points in the plane and combinatorics. Let ... SL(2,C) be a finite subgroup, and let Sn be the symmetric group on n letters. We study finite dimensional representations of the wreath product symplectic reflection algebra ... of …
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Border Basis Schemes
… K-vector space basis of P/I. The O-border basis scheme is a scheme that parametrizes all zero-dimensional ideals that have an O-border basis. In general, the O-border basis scheme is not an affine space. Subsequently, in [Huib09] it is proved that if an order ideal with "d" elements is defined in …
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Gromov-Witten theory in dimensions two and three
… the Gromov-Witten theory of Nakamura's G- Hilbert scheme, which is a preferred Calabi-Yau resolution of the polyhedral singularity C3/G. The classical McKay correspondence determines the (classical) cohomology of this resolution in terms of the representation theory of G. We express the …
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Gopakumar-Vafa invariant and Macdonald formula
In this thesis, I will introduce the Gopakumar-Vafa(GV) invariant and show one calculation on the nonreduced cycle. The GV invariant is an integral invariant predicted by physicist that counts the number of curves inside a given Calabi-Yau threefold. The definition has been conjectured by …
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Shifted symplectic structures and derived moduli spaces
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-02-04 without embargo terms