Algebraic Geometry Seminar
Kevin Tucker
UIC
Plus-pure thresholds of some cusp-like singularities
Abstract: The log canonical threshold (lct) is an important numerical invariant of singularities in complex algebraic geometry, with analytic origins. Via standard reduction to characteristic $p>0$ techniques, it is closely related to the $F$-pure threshold in positive characteristic defined in terms of the Frobenius endomorphism. These equal characteristic thresholds admit an analogue in the
developing theory of singularities in mixed characteristic, which is known as the plus-pure threshold. In this talk, I will review these notions and discuss a computation of the plus-pure thresholds of some mixed characteristic cusp-like singularities (such as $p^2 + x^3 \in \mathbb{Z}_p[[ x ]]$). This talk is based on joint work with Hanlin Cai, Suchitra Pande, Eamon Quinlan-Gallego, and Karl Schwede.
Monday January 27, 2025 at 3:00 PM in 636 SEO