DCC conjecture for volumes of RDP orbifold pairs

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Let (X,C)(X,C) be an orbifold pair on a rational double point, with boundary

C=∑i(1/ni)Ci.C=\sum_i (1/n_i)C_i.

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

1/3528=1/(2⋅422).1/3528=1/(2\cdot 42^2).

This is the proposed restriction to Gorenstein log terminal surface singularities after examples show that volumes of general Gorenstein orbifold pairs can form a strictly decreasing sequence. The supplied context does not state whether the claim has been proved or disproved.

References

Primary source

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

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