English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

The geometric objects of study in this paper are K3 surfaces which admit apolarization by the unique even unimodular lattice of signature (1,17). Astandard Hodge-theoretic observation about this special class of K3 surfaces isthat their polarized Hodge structures are identical with the polarized Hodgestructures of abelian surfaces that are cartesian products of elliptic curves.Earlier work of the first two authors gives an explicit normal form andconstruction of the moduli space for these surfaces. In the present work, thisnormal form is used to derive Picard-Fuchs differential equations satisfied byperiods of these surfaces. We also investigate the subloci of the moduli spaceon which the polarization is enhanced. In these cases, we derive informationabout the Picard-Fuchs differential equations satisfied by periods of thesesubfamilies, and we relate this information to the theory of genus zeroquotients of the upper half-plane by Moonshine groups. For comparison, we alsoexamine the analogous theory for elliptic curves in Weierstrass form.

Normal Forms, K3 Surface Moduli, and Modular Parametrizations