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Compatibility of Hodge Theory on Alexander Modules
Eva Elduque, Moisés Herradón Cueto
Let be a smooth connected complex algebraic variety, and let be an algebraic map. To the pair one can associate an infinite cyclic cover $U^f…
Hodge Theory of Abelian Covers
Eva Elduque, Moisés Herradón Cueto
Motivated by classical Alexander invariants of affine hypersurface complements, we endow certain finite dimensional quotients of the homology of abelian covers of complex algebraic…
Eigenspace Decomposition of Mixed Hodge Structures on Alexander Modules
Eva Elduque, Moisés Herradón Cueto
In previous work jointly with Geske, Maxim and Wang, we constructed a mixed Hodge structure (MHS) on the torsion part of Alexander modules, which generalizes the MHS on the cohomol…
Alexander modules, Mellin transformation and variations of mixed Hodge structures
Eva Elduque, Moisés Herradón Cueto, Laurenţiu Maxim +1
To any complex algebraic variety endowed with a morphism to a complex affine torus we associate multivariable cohomological Alexander modules, and define natural mixed Hodge struct…
Hodge theory on Alexander invariants -- a survey
Eva Elduque, Christian Geske, Moisés Herradón Cueto +2
We survey recent developments in the study of Hodge theoretic aspects of Alexander-type invariants associated with smooth complex algebraic varieties.
The local information of difference equations
Moisés Herradón Cueto
We give a definition for the restriction of a difference module on the affine line to a formal neighborhood of an orbit, trying to mimic the analogous definition and properties for…
An explicit quasiplatonic curve with non-abelian moduli field
Moisés Herradón Cueto
We give an example of a regular dessin d'enfant whose field of moduli is not an abelian extension of the rational numbers, namely it is the field generated by a cubic root of 2. Th…
The field of moduli and fields of definition of dessins d'enfants
Moises Herradon Cueto
We introduce dessins d'enfants from the various existing points of view: As topological covering spaces, as surfaces with triangulations, and as algebraic curves with functions ram…