Compact moduli spaces of stable sheaves over non-algebraic surfaces.
Birational models for varieties of Poncelet curves.
Vector bundles on blown-up Hopf surfaces
We show that certain moduli spaces of vector bundles over blown-up primary Hopf surfaces admit no compact components. These are the moduli spaces used by Andrei Teleman in his work on the classification of class VII surfaces.
On the Kähler Rank of Compact Complex Surfaces
Harvey and Lawson introduced the Kähler rank and computed it in connection to the cone of positive exact currents of bidimension for many classes of compact complex surfaces. In this paper we extend these computations to the only further known class of surfaces not considered by them, that of Kato surfaces. Our main tool is the reduction to the dynamics of associated holomorphic contractions .
A class of non-algebraic threefolds
Let be a compact complex nonsingular surface without curves, and a holomorphic vector bundle of rank 2 on . It turns out that the associated projective bundle has no divisors if and only if is “strongly” irreducible. Using the results concerning irreducible bundles of [Banica-Le Potier, J. Crelle, 378 (1987), 1-31] and [Elencwajg- Forster, Annales Inst. Fourier, 32-4 (1982), 25-51] we give a proof of existence for bundles which are strongly irreducible.
On the Petersson-Weil metric for the moduli space of Hermite-Einstein bundles and its curvature.
Non-Kähler compact complex manifolds associated to number fields
For algebraic number fields with real and complex embeddings and “admissible” subgroups of the multiplicative group of integer units of we construct and investigate certain -dimensional compact complex manifolds . We show among other things that such manifolds are non-Kähler but admit locally conformally Kähler metrics when . In particular we disprove a conjecture of I. Vaisman.
Maximal rationally connected fibrations and movable curves
A well known result of Miyaoka asserts that a complex projective manifold is uniruled if its cotangent bundle restricted to a general complete intersection curve is not nef. Using the Harder-Narasimhan filtration of the tangent bundle, it can moreover be shown that the choice of such a curve gives rise to a rationally connected foliation of the manifold. In this note we show that, conversely, a movable curve can be found so that the maximal rationally connected fibration of the manifold may be recovered...
Une caractérisation des surfaces d'Inoue-Hirzebruch
On montre que parmi les surfaces compactes complexes de classe avec , les surfaces d’Inoue-Hirzebruch sont caractérisées par le fait qu’elles possèdent deux champs de vecteurs tordus. Ce résultat est un pas vers la compréhension des feuilletages sur les surfaces .
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