Modularity of Maschke's octic and Calabi-Yau threefold
Matthias Schuett
TL;DR
This paper proves the modularity of Maschke's octic and related Calabi-Yau threefolds, confirming conjectures by Bini and van Geemen through automorphisms and K3 surface isogenies.
Contribution
It establishes the modularity of specific Calabi-Yau threefolds derived from Maschke's octic, using novel automorphism and isogeny techniques.
Findings
Confirmed modularity of Maschke's octic
Proved modularity of associated Calabi-Yau threefolds
Validated conjectures by Bini and van Geemen
Abstract
We prove the modularity of Maschke's octic and two Calabi-Yau threefolds derived from it as double octic and quotient thereof by the Heisenberg group, as conjectured by Bini and van Geemen. The proofs rely on automorphisms of the varieties and isogenies of K3 surfaces.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology