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 Plus annual

Presents the access of premium content as premium feature

Premium Content

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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let k be a field and f be a Siegel modular form of weight h \geq 0 and genusg>1 over k. Using f, we define an invariant of the k-isomorphism class of aprincipally polarized abelian variety (A,a)/k of dimension g. Moreover when(A,a) is the Jacobian of a smooth plane curve, we show how to associate to f aclassical plane invariant. As straightforward consequences of theseconstructions, when g=3 and k is a subfield of the complex field, we obtain (i)a new proof of a formula of Klein linking the modular form \chi_{18} to thesquare of the discriminant of plane quartics ; (ii) a proof that one can decidewhen (A,a) is a Jacobian over k by looking whether the value of \chi_{18} at(A,a) is a square in k. This answers a question of J.-P. Serre. Finally, westudy the possible generalizations of this approach for g>3.

Jacobians among Abelian threefolds: a formula of Klein and a question of Serre