UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

March 03, 2020

939 Evans Hall

3:45PM: The Belyi degree of a curve is computable

John Voight

We exhibit an algorithm that, given input a curve over a number field, computes as output the minimal degree of a Belyi map from the curve to the projective line. We discuss in detail the example of the Fermat curve of degree four and genus three.

5:00PM: A Riemann-Hurwitz-Plucker Formula

Adrian Zahariuc

The classical Riemann-Hurwitz and Plucker formulas count the number of ramification points of maps from projective curves into other curves and projective spaces respectively, and overlap in the case of maps to the projective line. In this talk, after reviewing these two formulas, I will state a common generalization which applies to maps from curves into arbitrary projective varieties, with ramification defined relative to an arbitrary flat family of divisors on the target. (This is joint work with Brian Osserman.)

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