Twisted de Rham complex for toric Calabi-Yau complete intersections and flat F-manifold structures

2023/12/28 by Park, Jeehoon, Park, Junyeong
#14F25 (primary) #14J32 #14J33 #14J81 #32S25 #81T70 (secondary) #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2312.17144

Abstract

We describe the primitive middle-dimensional cohomology ℍ of a compact simplicial toric complete intersection variety in terms of a twisted de Rham complex. Then this enables us to construct a concrete algorithm of formal flat F-manifold structures on ℍ in the Calabi-Yau case by using the techniques of \citePark23, which turn the twisted de Rham complex into a quantization dGBV (differential Gerstenhaber-Batalin-Vilkovisky) algebra and seek for an algorithmic solution to an associated weak primitive form.

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