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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 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...

On orbits of the automorphism group on an affine toric variety

Ivan Arzhantsev, Ivan Bazhov (2013)

Open Mathematics

Let X be an affine toric variety. The total coordinates on X provide a canonical presentation X ¯ X of X as a quotient of a vector space X ¯ by a linear action of a quasitorus. We prove that the orbits of the connected component of the automorphism group Aut(X) on X coincide with the Luna strata defined by the canonical quotient presentation.

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