6533b833fe1ef96bd129c334

RESEARCH PRODUCT

Modular Calabi-Yau threefolds of level eight

Christian MeyerSławomir Cynk

subject

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

description

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.

yearjournalcountryeditionlanguage
2005-04-05
https://dx.doi.org/10.48550/arxiv.math/0504070