Results 1 to 10 of about 405 (48)
Bialynicki-Birula schemes in higher dimensional Hilbert schemes of points and monic functors [PDF]
Épijournal de Géométrie Algébrique, 2021 The Bialynicki-Birula strata on the Hilbert scheme $H^n(\mathbb{A}^d)$ are smooth in dimension $d=2$. We prove that there is a schematic structure in higher dimensions, the Bialynicki-Birula scheme, which is natural in the sense that it represents a ...
Laurent Evain, Mathias Lederer
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$G$-fixed Hilbert schemes on $K3$ surfaces, modular forms, and eta products [PDF]
Épijournal de Géométrie Algébrique, 2022 Let $X$ be a complex $K3$ surface with an effective action of a group $G$ which preserves the holomorphic symplectic form. Let $$ Z_{X,G}(q) = \sum_{n=0}^{\infty} e\left(\operatorname{Hilb}^{n}(X)^{G} \right)\, q^{n-1} $$ be the generating function for ...
Jim Bryan, Ádám Gyenge
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The space of twisted cubics [PDF]
Épijournal de Géométrie Algébrique, 2021 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-
Katharina Heinrich +2 more
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Chow transformation of coherent sheaves
Complex Manifolds, 2023 We define a dual of the Chow transformation of currents on any complex projective manifold. This integral transformation is a factor of a left inverse of the Chow transformation and its composition with the Chow transformation is a right inverse of a ...
Méo Michel
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Torus actions, Morse homology, and the Hilbert scheme of points on affine space [PDF]
Épijournal de Géométrie Algébrique, 2021 We formulate a conjecture on actions of the multiplicative group in motivic homotopy theory. In short, if the multiplicative group G_m acts on a quasi-projective scheme U such that U is attracted as t approaches 0 in G_m to a closed subset Y in U, then ...
Burt Totaro
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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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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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Hyperkähler geometry of rational curves in twistor spaces
Complex Manifolds, 2022 We investigate the pseudo-hyperkähler geometry of higher degree rational curves in the twistor space of a hyperkähler 4-manifold.
Bielawski Roger, Zhang Naizhen
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