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Invariance for multiples of the twisted canonical bundle

Benoît Claudon (2007)

Annales de l’institut Fourier

Let 𝒳 → Δ a smooth projective family and ( L , h ) a pseudo-effective line bundle on 𝒳 (i.e. with a non-negative curvature current Θ h L ). In its works on invariance of plurigenera, Y.-T. Siu was interested in extending sections of m K 𝒳 0 + L (defined over the central fiber of the family 𝒳 0 ) to sections of m K 𝒳 + L . In this article we consider the following problem: to extend sections of m ( K 𝒳 + L ) . More precisely, we show the following result: assuming the triviality of the multiplier ideal sheaf ℐ ( 𝒳 0 , h | 𝒳 0 ) , any section of m ( K 𝒳 0 + L ) extends to 𝒳  ; in other...

Invariant properties of the generalized canonical mappings

Stanisław Janeczko (1999)

Banach Center Publications

One of the fundamental objectives of the theory of symplectic singularities is to study the symplectic invariants appearing in various geometrical contexts. In the paper we generalize the symplectic cohomological invariant to the class of generalized canonical mappings. We analyze the global structure of Lagrangian Grassmannian in the product symplectic space and describe the local properties of generic symplectic relations.

Invariants of translation surfaces

Pascal Hubert, Thomas A. Schmidt (2001)

Annales de l’institut Fourier

We definite invariants of translation surfaces which refine Veech groups. These aid in exact determination of Veech groups. We give examples where two surfaces of isomorphic Veech group cannot even share a common tree of balanced affine coverings. We also show that there exist translation surfaces of isomorphic Veech groups which cannot affinely cover any common surface. We also extend a result of Gutkin and Judge and thereby give the first examples of noncompact Fuchsian...

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