Real Enriques Surfaces, Issue 1746This is the first attempt of a systematic study of real Enriques surfaces culminating in their classification up to deformation. Simple explicit topological invariants are elaborated for identifying the deformation classes of real Enriques surfaces. Some of theses are new and can be applied to other classes of surfaces or higher-dimensional varieties. Intended for researchers and graduate students in real algebraic geometry it may also interest others who want to become familiar with the field and its techniques. The study relies on topology of involutions, arithmetics of integral quadratic forms, algebraic geometry of surfaces, and the hyperkähler structure of K3-surfaces. A comprehensive summary of the necessary results and techniques from each of these fields is included. Some results are developed further, e.g., a detailed study of lattices with a pair of commuting involutions and a certain class of rational complex surfaces. |
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Real Enriques Surfaces Alexander Degtyarev,Ilia Itenberg,Viatcheslav Kharlamov No preview available - 2014 |
Common terms and phrases
algebraic automorphism bilinear form C₁ characteristic class coarse type conj conjugate connected components Corollary corresponding decomposition defined deformation classes Del Pezzo surface Denote determined discr divisor Donaldson's trick double covering DPN-pair element elliptic pencil exact sequence fibers fixed point genus gluing H¹(X halves hence homology homomorphism induced intersection involution isometry isomorphism K3-surface Kähler lattice Lemma M-curve multiplication nondegenerate nonempty nonorientable nonsingular nonsingular real orientable orthogonal pair Pezzo surface Pic(X Poincaré duality Pontrjagin-Viro form Proof pull-back quadratic form quadrics quartic rational surface real curve real Enriques surfaces real structure respectively root scheme S₁ singular points space spectral sequence statement follows subgroup tangent Theorem topological type type Iu unique V₁ V₁US V₂ vector w₁