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The Kuranishi space of complex parallelisable nilmanifolds

Sönke Rollenske (2011)

Journal of the European Mathematical Society

We show that the deformation space of complex parallelisable nilmanifolds can be described by polynomial equations but is almost never smooth. This is remarkable since these manifolds have trivial canonical bundle and are holomorphic symplectic in even dimension. We describe the Kuranishi space in detail in several examples and also analyse when small deformations remain complex parallelisable.

The Local Torelli Theorem. I. Complete Intersection.

C. Peters (1975)

Mathematische Annalen

The local Torelli-theorem. II : cyclic branched coverings

C. A. M. Peters (1976)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

The mapping class group of a generic quadratic rational map and automorphisms of the 2-shift.

Linda Keen, Lisa R. Goldberg (1990)

Inventiones mathematicae

The moduli and the global period mapping of surfaces with $K^{2} = p_{g} = 1$ : a counterexample to the global Torelli problem

F. Catanese (1980)

Compositio Mathematica

The moduli of quotients of a compact complex space.

H.W. Schuster, A. Vogt (1986)

Journal für die reine und angewandte Mathematik

The moduli space of Riemann surfaces is Kähler hyperbolic.

McMullen, Curtis T. (2000)

Annals of Mathematics. Second Series

The Moduli Spaces of Vector Bundles over an Algebraic Curve.

S. Ramanan (1973)

Mathematische Annalen

The monodromy groups of Schwarzian equations on closed Riemann surfaces.

Gallo, Daniel, Kapovich, Michael, Marden, Albert (2000)

Annals of Mathematics. Second Series

The Monodromy Weight Filtration for a Several Variables Degeneration of Hodge Structures of Weight Two.

Eduardo H. Cattani, Aroldo G. Kaplan (1979)

Inventiones mathematicae

The Mumford conjecture

Geoffrey Powell (2004/2005)

Séminaire Bourbaki

The Mumford Conjecture asserts that the rational cohomology of the stable moduli space of Riemann surfaces is a polynomial algebra on the Mumford-Morita-Miller characteristic classes; this can be reformulated in terms of the classifying space $B Γ_{\infty}$ derived from the mapping class groups. The conjecture admits a topological generalization, inspired by Tillmann’s theorem that $B Γ_{\infty}$ admits an infinite loop space structure after applying Quillen’s plus construction. The text presents the proof by Madsen and...

The New Estimate for the Subbundles Ej and Its Application to the Deformation of the Boundaries of Strongly Pseudo Convex Domains.

Takao Akahori (1981)

Inventiones mathematicae

The New Neumann Operator Associated with Deformations of Strongly Pseudo Convex Domains and Its Application to Deformation Theory.

Takao Akahori (1982)

Inventiones mathematicae

Currently displaying 21 – 40 of 58

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Displaying 21 – 40 of 58

The Kuranishi space of complex parallelisable nilmanifolds

The Local Torelli Theorem. I. Complete Intersection.

The local Torelli-theorem. II : cyclic branched coverings

The mapping class group of a generic quadratic rational map and automorphisms of the 2-shift.

The moduli and the global period mapping of surfaces with $K^{2} = p_{g} = 1$ : a counterexample to the global Torelli problem

The moduli of quotients of a compact complex space.

The moduli space of Riemann surfaces is Kähler hyperbolic.

The Moduli Spaces of Vector Bundles over an Algebraic Curve.

The monodromy groups of Schwarzian equations on closed Riemann surfaces.

The Monodromy Weight Filtration for a Several Variables Degeneration of Hodge Structures of Weight Two.

The Mumford conjecture

The New Estimate for the Subbundles Ej and Its Application to the Deformation of the Boundaries of Strongly Pseudo Convex Domains.

The New Neumann Operator Associated with Deformations of Strongly Pseudo Convex Domains and Its Application to Deformation Theory.

The nilpotent part and distinguished form of resonant vector fields or diffeomorphisms

The outside of the Teichmüller space of punctured tori in Maskit's embedding.

The Picard group of the moduli of higher spin curves.

The Poisson Boundary of the Mapping Class Group and of Teichmüller Space

The Prym vector bundle and Gunning vector bundle over the Teichmüller space.

The singularities of Yang-Mills connections for bundles on a surface.

The space of quasisymmetric mappings.

Currently displaying 21 – 40 of 58