Maximal Mordell-Weil lattices of fibred surfaces with
On del Pezzo fibrations
On the arithmetic of genus two fibrations
On the genus of reducible surfaces and degenerations of surfaces
We deal with a reducible projective surface with so-called Zappatic singularities, which are a generalization of normal crossings. First we compute the -genus of , i.e. the dimension of the vector space of global sections of the dualizing sheaf . Then we prove that, when is smoothable, i.e. when is the central fibre of a flat family parametrized by a disc, with smooth general fibre, then the -genus of the fibres of is constant.
Presentation of hyperelliptic periodic monodromies and splitting families.
Pre-Tango structures and uniruled varieties
The pre-Tango structure is an ample invertible sheaf of locally exact differentials on a variety of positive characteristic. It is well known that pre-Tango structures on curves often induce pathological uniruled surfaces. We show that almost all pre-Tango structures on varieties induce higher-dimensional pathological uniruled varieties, and that each of these uniruled varieties also has a pre-Tango structure. For this purpose, we first consider the p-closed rational vector field induced...
Singular open book structures from real mappings
We define open book structures with singular bindings. Starting with an extension of Milnor’s results on local fibrations for germs with nonisolated singularity, we find classes of genuine real analytic mappings which yield such open book structures.
Sur les équations différentielles algébriques admettant des solutions avec une singularité essentielle
On démontre qu'une feuille transcendante d'un feuilletage analytique sur une surface fibrée doit intersecter toute courbe algébrique non invariante et non contenue dans une réunion de fibres de la fibration; comme application on montre qu'une équation différentielle algébrique qui possède une solution locale avec une singularité essentielle n'a pas de ramification mobile, ce qui généralise les théorèmes de Malmquist et Yosida.
Surface bundles over surfaces of small genus.
The automorphism group of
The paper studies fiber type morphisms between moduli spaces of pointed rational curves. Via Kapranov’s description we are able to prove that the only such morphisms are forgetful maps. This allows us to show that the automorphism group of is the permutation group on elements as soon as .
The Hodge theory of algebraic maps
The variety of dual mock-Lie algebras
We classify all complex - and -dimensional dual mock-Lie algebras by the algebraic and geometric way. Also, we find all non-trivial complex -dimensional dual mock-Lie algebras.
Towards a new interpretation of Milnor's number.
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Variétés rationnellement connexes
Vector bundles on plane cubic curves and the classical Yang–Baxter equation
In this article, we develop a geometric method to construct solutions of the classical Yang–Baxter equation, attaching a family of classical -matrices to the Weierstrass family of plane cubic curves and a pair of coprime positive integers. It turns out that all elliptic -matrices arise in this way from smooth cubic curves. For the cuspidal cubic curve, we prove that the obtained solutions are rational and compute them explicitly. We also describe them in terms of Stolin’s classication and prove...