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Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs

Victor V. Batyrev (1999)

Journal of the European Mathematical Society

Using non-Archimedian integration over spaces of arcs of algebraic varieties, we define stringy Euler numbers associated with arbitrary Kawamata log-terminal pairs. There is a natural Kawamata log-terminal pair corresponding to an algebraic variety V having a regular action of a finite group G . In this situation we show that the stringy Euler number of this pair coincides with the physicists’ orbifold Euler number defined by the Dixon-Harvey-Vafa-Witten formula. As an application, we prove a conjecture...

Non-deformability of entire curves in projective hypersurfaces of high degree

Olivier Debarre, Gianluca Pacienza, Mihai Păun (2006)

Annales de l’institut Fourier

In this article, we prove that there does not exist a family of maximal rank of entire curves in the universal family of hypersurfaces of degree d 2 n in the complex projective space n . This can be seen as a weak version of the Kobayashi conjecture asserting that a general projective hypersurface of high degree is hyperbolic in the sense of Kobayashi.

Non-embeddability of general unipotent diffeomorphisms up to formal conjugacy

Javier Ribón (2009)

Annales de l’institut Fourier

The formal class of a germ of diffeomorphism ϕ is embeddable in a flow if ϕ is formally conjugated to the exponential of a germ of vector field. We prove that there are complex analytic unipotent germs of diffeomorphisms at n ( n > 1 ) whose formal class is non-embeddable. The examples are inside a family in which the non-embeddability is of geometrical type. The proof relies on the properties of some linear functional operators that we obtain through the study of polynomial families of diffeomorphisms...

Non-embeddable 1 -convex manifolds

Jan Stevens (2014)

Annales de l’institut Fourier

We show that every small resolution of a 3-dimensional terminal hypersurface singularity can occur on a non-embeddable 1 -convex manifold.We give an explicit example of a non-embeddable manifold containing an irreducible exceptional rational curve with normal bundle of type ( 1 , - 3 ) . To this end we study small resolutions of c D 4 -singularities.

Non-holomorphic functional calculus for commuting operators with real spectrum

Mats Andersson, Bo Berndtsson (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We consider n -tuples of commuting operators a = a 1 , ... , a n on a Banach space with real spectra. The holomorphic functional calculus for a is extended to algebras of ultra-differentiable functions on n , depending on the growth of exp ( i a · t ) , t n , when | t | . In the non-quasi-analytic case we use the usual Fourier transform, whereas for the quasi-analytic case we introduce a variant of the FBI transform, adapted to ultradifferentiable classes.

Non-isotropic Hausdorff capacity of exceptional sets for pluri-Green potentials in the unit ball of ℂⁿ

Kuzman Adzievski (2006)

Annales Polonici Mathematici

We study questions related to exceptional sets of pluri-Green potentials V μ in the unit ball B of ℂⁿ in terms of non-isotropic Hausdorff capacity. For suitable measures μ on the ball B, the pluri-Green potentials V μ are defined by V μ ( z ) = B l o g ( 1 / | ϕ z ( w ) | ) d μ ( w ) , where for a fixed z ∈ B, ϕ z denotes the holomorphic automorphism of B satisfying ϕ z ( 0 ) = z , ϕ z ( z ) = 0 and ( ϕ z ϕ z ) ( w ) = w for every w ∈ B. If dμ(w) = f(w)dλ(w), where f is a non-negative measurable function of B, and λ is the measure on B, invariant under all holomorphic automorphisms of B, then V μ ...

Non-Kähler compact complex manifolds associated to number fields

Karl Oeljeklaus, Matei Toma (2005)

Annales de l’institut Fourier

For algebraic number fields K with s > 0 real and 2 t > 0 complex embeddings and “admissible” subgroups U of the multiplicative group of integer units of K we construct and investigate certain ( s + t ) -dimensional compact complex manifolds X ( K , U ) . We show among other things that such manifolds are non-Kähler but admit locally conformally Kähler metrics when t = 1 . In particular we disprove a conjecture of I. Vaisman.

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