The index conjecture for klt log Calabi–Yau pairs with positive boundary

Let dd be a natural number and let R\mathfrak{R} be a finite set of rational numbers. Let (X,B)(X,B) be a projective klt log Calabi–Yau pair of dimension dd, with B>0B>0, coefficients of BB in R\mathfrak{R}, and

KX+BQ0.K_X+B\sim_\mathbb Q0.

The klt index conjecture. There exists a positive integer nn, depending only on dd and R\mathfrak{R}, such that

n(KX+B)0.n(K_X+B)\sim 0.

Together with the absolute index conjecture, this forms the index conjecture for klt log Calabi–Yau pairs. The source gives no resolution status for this positive-boundary case.

Sources & referencesView supporting material

Primary source

Yanning Xu, “Some Results about the Index Conjecture for log Calabi-Yau Pairs”, arXiv:1905.00297 (2019).

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