Title: The F-signature function on the big cone
Abstract: The F-signature is a numerical invariant of singularities in positive characteristic that measures asymptotic properties of the Frobenius map. While initially studied as an algebraic invariant of local rings, there has been recent interest in the geometric and global aspects of this invariant. In previous work with Seungsu Lee, we studied the F-signature of a projective variety as a continuous function on the ample cone. In this talk, I will discuss continuation of our work where we extend the F-signature function to the big cone. The results include existence of the F-signature for big divisors, continuity and positivity of the F-signature on the big cone and transformation rules under birational contractions for big and semi-ample divisors. As a key tool, we also study similar properties for the Frobenius-alpha invariant. The geometric aspects of our techniques will be presented and emphasized.
Yuchen Liu
(847) 491-5553
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