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On the genus of reducible surfaces and degenerations of surfaces

Alberto Calabri, Ciro Ciliberto, Flaminio Flamini, Rick Miranda (2007)

Annales de l’institut Fourier

We deal with a reducible projective surface X with so-called Zappatic singularities, which are a generalization of normal crossings. First we compute the ω -genus p ω ( X ) of X , i.e. the dimension of the vector space of global sections of the dualizing sheaf ω X . Then we prove that, when X is smoothable, i.e. when X is the central fibre of a flat family π : 𝒳 → Δ parametrized by a disc, with smooth general fibre, then the ω -genus of the fibres of π is constant.

Pre-Tango structures and uniruled varieties

Yoshifumi Takeda (2007)

Colloquium Mathematicae

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

Raimundo Araújo dos Santos, Ying Chen, Mihai Tibăr (2013)

Open Mathematics

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

Ivan Pan, Marcos Sebastiani (2001)

Annales de l’institut Fourier

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.

The automorphism group of M ¯ 0 , n

Andrea Bruno, Massimiliano Mella (2013)

Journal of the European Mathematical Society

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 M ¯ 0 , n is the permutation group on n elements as soon as n ≥ 5 .

The variety of dual mock-Lie algebras

Luisa M. Camacho, Ivan Kaygorodov, Viktor Lopatkin, Mohamed A. Salim (2020)

Communications in Mathematics

We classify all complex 7 - and 8 -dimensional dual mock-Lie algebras by the algebraic and geometric way. Also, we find all non-trivial complex 9 -dimensional dual mock-Lie algebras.

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Shigeharu Takayama (0)

Annales de l’institut Fourier

Vector bundles on plane cubic curves and the classical Yang–Baxter equation

Igor Burban, Thilo Henrich (2015)

Journal of the European Mathematical Society

In this article, we develop a geometric method to construct solutions of the classical Yang–Baxter equation, attaching a family of classical r -matrices to the Weierstrass family of plane cubic curves and a pair of coprime positive integers. It turns out that all elliptic r -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...

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