The boundedness-of-index conjecture for canonical Q-Fano varieties

Let WW be a canonical Q{\bf Q}-Fano variety of dimension nn, meaning that WW has at worst canonical singularities and KW1K_W^{-1} is an ample Q{\bf Q}-Cartier divisor. Its index r(W)r(W) is the maximal positive rational number such that KW1=Lr(W)K_W^{-1}=L^{\otimes r(W)} for some Cartier divisor LL.

Boundedness-of-index conjecture. The set of possible values of r(W)r(W) for canonical Q{\bf Q}-Fano varieties WW of dimension nn is finite.

The source presents this as the additional conjectural input for deriving the Spectrum Conjecture from the Minimal Model Program. The supplied text gives no resolution status.

Sources & referencesView supporting material

Primary source

Victor V. Batyrev and Yu. Tschinkel, “Tamagawa numbers of polarized algebraic varieties”, arXiv:alg-geom/9712002 (1997).

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