Smoothing conjecture and degree bound for Fano threefolds with cDV singularities

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Let VV be a Fano threefold with only cDV singularities. A smoothing means a deformation whose nearby fibers are smooth.

cDV smoothing conjecture. VV has a smoothing by a small deformation. In particular,

−KV3≤64.-K_V^3\le 64.

The source notes that the general bound −KV3≤72-K_V^3\le 72 is not sharp in the cDV case and expects the stronger bound 6464; the proposed smoothing statement is presented as a realistic conjecture.

References

Primary source

Yuri G. Prokhorov, “On the degree of Fano threefolds with canonical Gorenstein singularities”, arXiv:math/0405347 (2025).

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