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Comparison of Frobenius algebra structures on Calabi-Yau toric hypersurfaces (2504.06694v1)
Published 9 Apr 2025 in math.AG, math-ph, and math.MP
Abstract: We establish an isomorphism between two Frobenius algebra structures, termed CY and LG, on the primitive cohomology of a smooth Calabi--Yau hypersurface in a simplicial Gorenstein toric Fano variety. As an application of our comparison isomorphism, we observe the existence of a Frobenius manifold structure on a finite-dimensional subalgebra of the Jacobian algebra of a homogeneous polynomial which may exhibit a non-compact singularity locus.