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On meromorphic functions defined by a differential system of order 1

Tristan Torrelli (2004)

Bulletin de la Société Mathématique de France

Given a germ h of holomorphic function on ( n , 0 ) , we study the condition: “the ideal Ann 𝒟 1 / h is generated by operators of order1”. We obtain here full characterizations in the particular cases of Koszul-free germs and unreduced germs of plane curves. Moreover, we prove that this condition holds for a special type of hyperplane arrangements. These results allow us to link this condition to the comparison of de Rham complexes associated with h .

On meromorphic functions with maximal defect sum

Pham Duc Thoan, Le Thanh Tung (2011)

Annales Polonici Mathematici

The purpose of this article is twofold. The first is to give necessary conditions for the maximality of the defect sum. The second is to show that the class of meromorphic functions with maximal defect sum is very thin in the sense that deformations of meromorphic functions with maximal defect sum by small meromorphic functions are not meromorphic functions with maximal defect sum.

On metacyclic extensions

Masanari Kida (2012)

Journal de Théorie des Nombres de Bordeaux

Galois extensions with various metacyclic Galois groups are constructed by means of a Kummer theory arising from an isogeny of certain algebraic tori. In particular, our method enables us to construct algebraic tori parameterizing metacyclic extensions.

On moduli spaces of semistable sheaves on Enriques surfaces

Marcin Hauzer (2010)

Annales Polonici Mathematici

We describe some one-dimensional moduli spaces of rank 2 Gieseker semistable sheaves on an Enriques surface improving earlier results of H. Kim. In the case of a nodal Enriques surface the moduli spaces obtained are reducible for general polarizations. For unnodal Enriques surfaces we show how to reduce the study of moduli spaces of high even rank Gieseker semistable sheaves to low ranks. To prove this we use the method of K. Yoshioka who showed that in the odd rank case, one can reduce to rank...

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