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

The goal of this article is to provide an explicit algorithmic constructionof formal $F$-manifold structures, formal Frobenius manifold structures, andhigher residue pairings on the primitive middle-dimensional cohomology$\mathbb{H}$ of a smooth projective Calabi-Yau complete intersection variety$X$ defined by homogeneous polynomials $G_1(\underline x), \dots,G_k(\underline x)$. Our main method is to analyze a certain dGBV (differentialGerstenhaber-Batalin-Vilkovisky) algebra $\mathcal{A}$ obtained from thetwisted de Rham complex which computes $\mathbb{H}$. More explicitly, weintroduce a notion of \textit{a weak primitive form} associated to a solutionof the Maurer-Cartan equation of $\mathcal{A}$ and the Gauss-Manin connection,which is a weakened version of Saito's primitive form (\cite{Saito}). Inaddition, we provide an explicit algorithm for a weak primitive form based onthe Gr\"obner basis in order to achieve our goal. Our approach through the weakprimitive form can be viewed as a unifying link (based on Witten's gaugedlinear sigma model, \cite{W93}) between the Barannikov-Kontsevich's approach toFrobenius manifolds via dGBV algebras (non-linear topological sigma model,\cite{BK}) and Saito's approach to Frobenius manifolds via primitive forms andhigher residue pairings (Landau-Ginzburg model, \cite{ST}).

Smooth projective Calabi-Yau complete intersections and algorithms for their Frobenius manifolds and higher residue pairings