Compact hyperkähler manifolds: basic results

By D. Huybrechts. 2003

382 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/969a2876730fdad58985ca830e99781ac56fc7de

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Yuguang Zhang
2. Valentino Tosatti
3. Kieran G. O’Grady
4. E. Markman
5. Justin Sawon
6. Mark Gross
7. Keiji Oguiso
8. Franccois Charles

In Geometry and Topology

1. D. Huybrechts
2. E. Markman
3. Giovanni Mongardi
4. A. Sarti
5. Samuel Boissière
6. Keiji Oguiso
7. Yuguang Zhang
8. E. Looijenga

In Nuclear and High Energy Physics

1. Kieran G. O’Grady
2. E. Markman
3. Justin Sawon
4. Franccois Charles
5. R. Laza
6. Ulrike Riess
7. D. Guan
8. E. Looijenga

Citations in the corpus

• The moduli space of cubic fourfolds via the period map (2007, background): “A surjectivity type statement for irreducible symplectic fourfolds is known (see Huybrechts [22]), but the linear systems on symplectic fourfolds are not sufficiently understood to obtain a characterization of the image of the period map in this way.”
• Irreducible symplectic 4-folds and Eisenbud-Popescu-Walter sextics (2005, neutral): “A G ] 1 9”
• A survey of Torelli and monodromy results for holomorphic-symplectic varieties (2011, background): “(3) ([ Hu1 ], Theorem 4.3) Let (X1;h1) and (X2;h2) be two inseparable points of”
• Moduli of K3 Surfaces and Irreducible Symplectic Manifolds (2010, background): “Theorem 3.4 (Huybrechts) Let L be a lattice of an irreducible symplectic manifold and let ΩL be the associated period domain.”
• Lagrangian Fibrations of Holomorphic-Symplectic Varieties of K3[n]-Type (2013, background): “Hence, there exists an analytic correspondence Z ⊂ X × Y , Z = ∑ ki = 0 Z i in X × Y , of pure dimension 2 n , with the following properties, by results of Huybrechts [Hu1, Theorem 4.3] (see also [Ma5, Sec.”
• Collapsing of abelian fibred Calabi-Yau manifolds (2011, background): “Then Per is étale, and was proved to be surjective by Huybrechts in [21].”
• The Tate conjecture for K3 surfaces over finite fields (2012, background): “The second singular cohomology group of a complex irreducible holomorphic symplectic variety is endowed with a canonical form called the Beauville-Bogomolov form, see [4, 20].”
• Lectures on K3 Surfaces (2016, background): “A slightly shorter proof of the surjectivity using a less precise description of the Kähler cone (that generalizes to higher dimensions) can be found in [248].”