38.94192000792223, -92.32805562883608

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Title: The F-signature function on the ample cone of a globally F-regular variety.

 

Abstract: The F-signature of a strongly F-regular local ring R is an interesting invariant of its singularities. In this talk, we will discuss this invariant when R is the normalized homogeneous coordinate ring of a projective variety. In particular, we study how the F-signature varies as we vary the embedding of a fixed projective variety X into various projective spaces. For this purpose, we will introduce the F-signature function, a real valued function on the ample cone of X, and discuss its continuity properties. We will also present some analogies and comparisons to the well-known volume function, which records the Hilbert-Samuel multiplicities. This is joint work with Seungsu Lee.
 

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