The nef Cartier b-divisor determination conjecture

Let XX be a reduced integral noetherian excellent QQQQ-scheme and let DCDivQXD\in\operatorname{\mathbf{CDiv}}_{\mathbb{Q}}X be nef. A determination of DD is a modification f:YXf:Y\to X on which the b-divisor DD is represented by a Cartier divisor D(Y)D(Y); its center is the locus where DD is not Cartier on XX.

Nef Cartier b-divisor determination conjecture. If DCDivQXD\in\operatorname{\mathbf{CDiv}}_{\mathbb{Q}}X is nef, then there exists a determination of DD with center equal to the Cartier locus of ff.

This conjecture seeks a geometric determination with the smallest possible center for nef Cartier b-divisors. The supplied text does not state whether it has been resolved.

Sources & referencesView supporting material

Primary source

Kiran S. Kedlaya, “Good formal structures for flat meromorphic connections, III: Irregularity and turning loci”, arXiv:1308.5259 (2019).

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