DCC conjecture for volumes of orbifold pairs on rational double points

Let (X,C)(X,C) be an orbifold pair on a rational double point, where CC is a boundary of the form

C=i(1/ni)Ci.C=\sum_i (1/n_i)C_i.

DCC conjecture. The set of volumes of such orbifold pairs satisfies the descending chain condition, and its minimum nonzero value is

1/3528=(24242)1.1/3528=(2\cdot 42\cdot 42)^{-1}.

The paper motivates this claim by noting that volumes of general Gorenstein orbifold pairs need not satisfy the DCC, while the restriction to rational double points is expected to restore this property. The supplied context does not state whether the conjecture has been proved or disproved.

Sources & referencesView supporting material

Primary source

Jonathan Wahl, “The Volume of a Surface or Orbifold Pair”, arXiv:2312.14271 (2026).

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