Singularity-degeneration conjecture for Calabi–Yau zeta functions

Let Rv(t)R_{\mathbf{v}}(t) be the contribution to the zeta function associated with a monomial class v\mathbf{v}, and define the degree of a rational function by

deg(f/g)=deg(f)deg(g).\operatorname{deg}(f/g)=\operatorname{deg}(f)-\operatorname{deg}(g).

Singularity-degeneration conjecture. The degeneration of deg(Rv)\operatorname{deg}(R_{\mathbf{v}}) for each piece of the zeta function of a Calabi–Yau manifold at a singular point in moduli space is determined by the nature of the singularity. The source illustrates this with conifold and other singular loci, but gives no general resolution.

Sources & referencesView supporting material

Primary source

Shabnam N. Kadir, “The Arithmetic of Calabi–Yau Manifolds and Mirror Symmetry”, arXiv:hep-th/0409202 (2004).

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