DCC conjecture for volumes of orbifold pairs on rational double points
DCC conjecture for volumes of orbifold pairs on rational double points
Let be an orbifold pair on a rational double point, where is a boundary of the form
DCC conjecture. The set of volumes of such orbifold pairs satisfies the descending chain condition, and its minimum nonzero value is
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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