Erratum to the paper: Compact hyperkaehler manifolds: basic results

By D. Huybrechts. 2001

166 citations recorded by the source corpus.

This is an Erratum to the paper: Compact hyperkaehler manifolds: basic results. (alg-geom/9705025, Inv. math. 135). We give a correct proof of the projectivity criterion for hyperkaehler manifolds. We use a recent result of Demailly and Paun math.AG/0105176.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/4ce75b9142310dd162e22e618aa2ee966d86bbfa

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In Applied Mathematics

1. A. Rapagnetta
2. Kieran G. O’Grady
3. Giovanni Mongardi
4. E. Markman

In Geometry and Topology

1. Giovanni Mongardi
2. A. Rapagnetta
3. E. Markman
4. Kieran G. O’Grady
5. D. Huybrechts
6. A. Sarti
7. Samuel Boissière
8. Misha Verbitsky

Citations in the corpus

• The global moduli theory of symplectic varieties (2018, unknown): “We also prove analogs of results of Huybrechts [Huy99] and [BL16] on the inseparability of bimeromorphic symplectic varieties in moduli, including part (3) of Theorems 1.”
• On the Beauville form of the known irreducible symplectic varieties (2006, background): “By a theorem of Huybrechts (see Theorem 4.6 of [ 8 ]) birationally equivalent irreducible symplectic varieties are deformation equivalent.”
• Monodromy and birational geometry of O'Grady's sixfolds (2019, background): “1 of [9], holds for manifolds of OG6 type:”
• Integral generators for the cohomology ring of moduli spaces of sheaves over Poisson surfaces (2004, background): “Let M0 Λ be a connected component of MΛ, containing a marked Hilbert scheme (S[n],φ 0) of a K3 surface S. The Surjectivity Theorem states, that the restriction of the period map to M0 Λ is surjective [Hu3]. The group OΛ acts on MΛ, by changing the marking, and the period map is OΛ-equivariant. Fix a”
• IRREDUCIBLE SYMPLECTIC 4-FOLDS NUMERICALLY EQUIVALENT TO (K3)[2] (2008, methodology): “Huybrechts’ projectivity criterion [ 13 ]: since H1,1”
• INTEGRAL CONSTRAINTS ON THE MONODROMY GROUP OF THE HYPERKÄHLER RESOLUTION OF A SYMMETRIC PRODUCT OF A K3 SURFACE (2006, background): “mponent of MΛ, (X,φ) a marked pair in M0 Λ, and f an element of O+Λ. Choose a marked pair (Y,ψ) in M0 Λ, whose period satisfies P(Y,ψ) = f(P(X,φ)).Such a pair (Y,ψ) exists, by the Surjectivity Theorem [Hu2]. Lemma 4.6 Assume that Xsatisfies Condition 4.4. If fdoes not belong to W(Λ), then the pairs {Q”