Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: The maximal rank conjecture (Part II)

Seminar | September 4 | 5-6 p.m. | 939 Evans Hall

 Eric Larson, Stanford University

 Department of Mathematics

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 $\mathbb P^r$ via a general linear series of degree d. We then explain how results on the interpolation problem can be leveraged to prove this conjecture.