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Reid's general elephant conjecture for Q-Fano threefolds

Let XX be a Q\mathbb Q-Fano threefold, and let H∈∣−KX∣H\in|-K_X| be a generic section of the anticanonical divisor. Reid's general elephant conjecture. The surface HH has at worst canonical singularities. This conjecture is motivated by using anticanonical sections to classify Fano varieties; the source gives no resolution status.

Sources & referencesView supporting material

Primary source

M. Andreatta and M. Mella, “Morphisms of Projective Varieties from the viewpoint of Minimal Model Theory”, arXiv:math/0205224 (2002).

Additional references

3 papers in this index state this conjecture (1996–2002). The statement above is taken from the most recent of them; the others are arXiv:math/9912111, arXiv:alg-geom/9605002.

fano-varietiessingularity-theorythreefolds

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