UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

September 04, 2018

939 Evans Hall


3:45PM: The maximal rank conjecture (Part I)

Eric Larson

In the first hour, we discuss the problem of interpolation for curves in projective space: When does there exist a curve of degree d and genus g passing through n general points in P^r?

5:00PM: The maximal rank conjecture (Part II)

Eric Larson

In the second hour, we discuss the Maximal Rank Conjecture, a conjecture formulated originally by Severi in 1915 which prescribes a relationship between the "shape" of the parametric and Cartesian equations of curves in projective space --- that is, which gives the Hilbert function of a general curve of genus g, embedded in P^r via a general linear series of degree d. We then explain how results on the interpolation problem can be leveraged to prove this conjecture.

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