Results 21 to 30 of about 428 (65)
Small elementary components of Hilbert schemes of points
Forum of Mathematics, Sigma, 2023 We answer an open problem posed by Iarrobino, Hilbert scheme of points: Overview of last ten years. Proceedings of Symposia in Pure Mathematics, 46 (American Mathematical Society, Providence, RI, 1987), 297–320: Is there a component of the punctual ...
Matthew Satriano, Andrew P. Staal
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Forum of Mathematics, Sigma, 2021 We prove an equivalence between the Bryan-Steinberg theory of $\pi $-stable pairs on $Y = \mathcal {A}_{m-1} \times \mathbb {C}$ and the theory of quasimaps to $X = \text{Hilb}(\mathcal {A}_{m-1})$, in the form of an equality of K-theoretic equivariant
Henry Liu
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Extremal Gromov-Witten invariants of the Hilbert scheme of $3$ Points
Forum of Mathematics, Sigma, 2023 We determine all the extremal Gromov-Witten invariants of the Hilbert scheme of $3$ points on a smooth projective complex surface. Our result for the genus- $1$ case verifies a conjecture that we propose for the genus- $1$ extremal ...
Jianxun Hu, Zhenbo Qin
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Quot schemes and Fourier-Mukai transformation
Complex Manifolds, 2023 We consider several related examples of Fourier-Mukai transformations involving the quot scheme. A method of showing conservativity of these Fourier-Mukai transformations is described.
Biswas Indranil +3 more
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Higher rank K-theoretic Donaldson-Thomas Theory of points
Forum of Mathematics, Sigma, 2021 We exploit the critical structure on the Quot scheme $\text {Quot}_{{{\mathbb {A}}}^3}({\mathscr {O}}^{\oplus r}\!,n)$, in particular the associated symmetric obstruction theory, in order to study rank r K-theoretic Donaldson-Thomas (DT) invariants of ...
Nadir Fasola +2 more
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Enumeration of surfaces containing an elliptic quartic curve [PDF]
, 2014 A very general surface of degree at least four in projective space of dimension three contains no curves other than intersections with surfaces. We find a formula for the degree of the locus of surfaces of degree at least five which contain some elliptic
Cukierman, Fernando +2 more
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Higher rank sheaves on threefolds and functional equations [PDF]
Épijournal de Géométrie Algébrique, 2019 We consider the moduli space of stable torsion free sheaves of any rank on a smooth projective threefold. The singularity set of a torsion free sheaf is the locus where the sheaf is not locally free. On a threefold it has dimension $\leq 1$.
Amin Gholampour, Martijn Kool
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Nodal curves with general moduli on K3 surfaces [PDF]
, 2007 We investigate the modular properties of nodal curves on a low genus K3 surface. We prove that a general genus g curve C is the normalization of a d-nodal curve X sitting on a primitively polarized K3 surface S of degree 2p-2, for p any integer between 3
Flamini, Flaminio +3 more
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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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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
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