Displaying similar documents to “Invariance for multiples of the twisted canonical bundle”

A lossless reduction of geodesics on supermanifolds to non-graded differential geometry

Stéphane Garnier, Matthias Kalus (2014)

Archivum Mathematicum

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Let ℳ = ( M , 𝒪 ℳ ) be a smooth supermanifold with connection ∇ and Batchelor model 𝒪 ℳ ≅ Γ Λ E * . From ( ℳ , ∇ ) we construct a connection on the total space of the vector bundle E → M . This reduction of ∇ is well-defined independently of the isomorphism 𝒪 ℳ ≅ Γ Λ E * . It erases information, but however it turns out that the natural identification of supercurves in ℳ (as maps from ℝ 1 | 1 to ℳ ) with curves in E restricts to a 1 to 1 correspondence on geodesics. This bijection is induced by a natural identification of initial conditions for...

Numerical character of the effectivity of adjoint line bundles

Frédéric Campana, Vincent Koziarz, Mihai Păun (2012)

Annales de l’institut Fourier

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In this note we show that, for any log-canonical pair ( X , Δ ) , K X + Δ is ℚ -effective if its Chern class contains an effective ℚ -divisor. Then, we derive some direct corollaries.

Low pole order frames on vertical jets of the universal hypersurface

Joël Merker (2009)

Annales de l’institut Fourier

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For low order jets, it is known how to construct meromorphic frames on the space of the so-called vertical k -jets J vert k ( 𝒳 ) of the universal hypersurface 𝒳 ⊂ ℙ n + 1 × ℙ ( n + 1 + d ) ! ( ( n + 1 ) ! d ! ) - 1 parametrizing all projective hypersurfaces X ⊂ ℙ n + 1 ( ℂ ) of degree d . In 2004, for k = n , Siu announced that there exist two constants c n ≥ 1 and c n ′ ≥ 1 such that the twisted tangent bundle T J vert n ( 𝒳 ) ⊗ 𝒪 ℙ n + 1 ( c n ) ⊗ 𝒪 ℙ ( n + 1 + d ) ! ( ( n + 1 ) ! d ! ) - 1 ( c n ′ ) is generated at every point by its global sections. In...

Notes on prequantization of moduli of G -bundles with connection on Riemann surfaces

Andres Rodriguez (2004)

Annales mathématiques Blaise Pascal

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Let 𝒳 → S be a smooth proper family of complex curves (i.e. family of Riemann surfaces), and ℱ a G -bundle over 𝒳 with connection along the fibres 𝒳 → S . We construct a line bundle with connection ( ℒ ℱ , ∇ ℱ ) on S (also in cases when the connection on ℱ has regular singularities). We discuss the resulting ( ℒ ℱ , ∇ ℱ ) mainly in the case G = ℂ * . For instance when S is the moduli space of line bundles with connection over a Riemann surface X , 𝒳 = X × S , and ℱ is the Poincaré bundle over 𝒳 , we show that ( ℒ ℱ , ∇ ℱ ) provides a prequantization...

L 2 extension of adjoint line bundle sections

Dano Kim (2010)

Annales de l’institut Fourier

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We prove an extension theorem of Ohsawa-Takegoshi type for line bundle sections on a subvariety of general codimension in a normal projective variety. Our method of proof gives conditions to be satisfied for such extension in a general setting, while such conditions are satisfied when the subvariety is given by an appropriate multiplier ideal sheaf.