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Titlebook: Algebraic and Complex Geometry; In Honour of Klaus H Anne Frühbis-Krüger,Remke Nanne Kloosterman,Matthi Conference proceedings 2014 Springe

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McKay Correspondence over Non Algebraically Closed Fields,n this paper we show that these two phenomena are related and that there is a bijection between nontrivial irreducible representations and irreducible components of the exceptional divisor over non algebraically closed fields . of characteristic 0 as well.
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Lagrangian Fibrations of Holomorphic-Symplectic Varieties of ,3,-Type,dle . is effective. A determination of the semi-group of effective divisor classes on . follows, when . is projective. For a generic such pair ., not necessarily projective, we show that . is bimeromorphic to a Tate-Shafarevich twist of a moduli space of stable torsion sheaves, each with pure one dimensional support, on a .3 surface.
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2194-1009 moduli spaces and irreducible holomorphic symplectic manifolds were highlighted at the conference “Algebraic and Complex Geometry” held September 2012 in Hannover, Germany. These two subjects of recent ongoing progress belong to the most spectacular developments in Algebraic and Complex Geometry. I
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https://doi.org/10.1057/9780230289758 applications of this to (i) the counting of plane nodal curves through base points in special position, (ii) the irreducibility of Severi varieties of a general quartic surface, and (iii) the monodromy of the universal family of rational curves on quartic .3 surfaces.
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https://doi.org/10.1007/978-3-662-53666-7formation of the projectivised tangent bundle over a projective space is again of this type unless it is the projectivisation of a special unstable bundle over a projective space. Examples for these bundles are given in any dimension.
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,Limits of Pluri–Tangent Planes to Quartic Surfaces, applications of this to (i) the counting of plane nodal curves through base points in special position, (ii) the irreducibility of Severi varieties of a general quartic surface, and (iii) the monodromy of the universal family of rational curves on quartic .3 surfaces.
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Stability Conditions and Positivity of Invariants of Fibrations, methods involve different stability conditions. In dimension 2 we prove that there is a natural connection between them, related to a yet another stability condition, the linear stability. Finally we make some speculations and prove new results in higher dimension.
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