Search results for "double coverings"

showing 2 items of 2 documents

Infinitesimal deformations of double covers of smooth algebraic varieties

2003

The goal of this paper is to give a method to compute the space of infinitesimal deformations of a double cover of a smooth algebraic variety. The space of all infinitesimal deformations has a representation as a direct sum of two subspaces. One is isomorphic to the space of simultaneous deformations of the branch locus and the base of the double covering. The second summand is the subspace of deformations of the double covering which induce trivial deformations of the branch divisor. The main result of the paper is a description of the effect of imposing singularities in the branch locus. As a special case we study deformations of Calabi--Yau threefolds which are non--singular models of do…

14B07; 14J3014J30Direct sum14B07General MathematicsInfinitesimalMathematical analysisAlgebraic varietySymbolic computationLinear subspaceequisingular deformationsMathematics - Algebraic GeometryMathematics::Algebraic GeometryFOS: MathematicsProjective spaceGravitational singularityLocus (mathematics)Algebraic Geometry (math.AG)double coveringsMathematics
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Modular Calabi-Yau threefolds of level eight

2005

In the studies on the modularity conjecture for rigid Calabi-Yau threefolds several examples with the unique level 8 cusp form were constructed. According to the Tate Conjecture correspondences inducing isomorphisms on the middle cohomologies should exist between these varieties. In the paper we construct several examples of such correspondences. In the constructions elliptic fibrations play a crucial role. In fact we show that all but three examples are in some sense built upon two modular curves from the Beauville list.

Pure mathematicsConjectureMathematics - Number Theory14G1014J32General MathematicsModular formModular invariancemodular forms14G10; 14J32Cusp formModular curveAlgebraMathematics - Algebraic GeometryMathematics::Algebraic GeometryModular elliptic curveCalabi-YauFOS: MathematicsCalabi–Yau manifoldNumber Theory (math.NT)Tate conjectureAlgebraic Geometry (math.AG)MathematicsTate conjecturedouble coverings
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