Degeneration-conservation conjecture for coincident singularities

Let Rv(t)R_{\mathbf{v}}(t) be a contribution to the zeta function, and let the degree degeneration measure the decrease in deg(Rv)\operatorname{deg}(R_{\mathbf{v}}) caused by a singularity type. Degeneration-conservation conjecture. When two types of singularity coincide, the total degeneration in degree of each contribution is the sum of the degenerations caused by the individual singularity types. This is presented as a proposed rule for the combined singular loci in the octic family; the source gives no resolution status.

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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