F-pure threshold as a measure of singularities

Takagi and Watanabe introduced F-pure threshold as a “Frobenius analogue” of log canonical threshold from birational geometry, showed that F-pure threshold detects whether a local ring is singular, and explored its connections with other invariants. This local study of F-pure threshold, was subsequently further expanded by other authors. I will report on a joint work with Alessandro de Stefani and Luís Núñez-Betancourt, which instead takes the theory in a new direction by studying the geometric properties of F-pure threshold as a singularity measure.

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