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Non-uniruledness and the cancellation problem

Robert Dryło (2005)

Annales Polonici Mathematici

Using the notion of uniruledness we indicate a class of algebraic varieties which have a stronger version of the cancellation property. Moreover, we give an affirmative solution to the stable equivalence problem for non-uniruled hypersurfaces.

Non-zero constant Jacobian polynomial maps of ²

Nguyen Van Chau (1999)

Annales Polonici Mathematici

We study the behavior at infinity of non-zero constant Jacobian polynomial maps f = (P,Q) in ℂ² by analyzing the influence of the Jacobian condition on the structure of Newton-Puiseux expansions of branches at infinity of level sets of the components. One of the results obtained states that the Jacobian conjecture in ℂ² is true if the Jacobian condition ensures that the restriction of Q to the curve P = 0 has only one pole.

Numerical character of the effectivity of adjoint line bundles

Frédéric Campana, Vincent Koziarz, Mihai Păun (2012)

Annales de l’institut Fourier

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

Numerically trivial foliations

Thomas Eckl (2004)

Annales de l’institut Fourier

Given a positive singular hermitian metric of a pseudoeffective line bundle on a complex Kähler manifold, a singular foliation is constructed satisfying certain analytic analogues of numerical conditions. This foliation refines Tsuji’s numerically trivial fibration and the Iitaka fibration. Using almost positive singular hermitian metrics with analytic singularities on a pseudo-effective line bundle , a foliation is constructed refining the nef fibration. If the singularities of the foliation are...

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