Singularity-degeneration conjecture for Calabi–Yau zeta functions

About 22 years old · traced to

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.

References

Primary source

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

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.