A question of Mori and families of plane curves

Abstract: Consider a smooth family of hypersurfaces of degree d in P^{n+1}. An old question of Mori is: when is every smooth limit of this family also a hypersurface? While it is easy to construct examples where the answer is "no" when the degree d is composite, there are no known examples when d is prime and n>2! We will pose this as a conjecture (primality of degree is sufficient to ensure every smooth limit is a hypersurface, for n > 2). However, there are counterexamples when n=1 or 2. In this talk, we will propose a re-formulation of the conjecture that explains the failure in low dimensions, provide results in dimension one, and discuss a general approach to the problem using moduli spaces of pairs. This is joint work with David Stapleton.

algebraic geometrynumber theory

Audience: researchers in the topic

SFU NT-AG seminar

Series comments: The Number Theory and Algebraic Geometry (NT-AG) seminar is a research seminar dedicated to topics related to number theory and algebraic geometry hosted by the NT-AG group (Nils Bruin, Imin Chen, Stephen Choi, Katrina Honigs, Nathan Ilten, Marni Mishna).

We acknowledge the support of PIMS, NSERC, and SFU.

For Fall 2025, the organizers are Katrina Honigs and Peter McDonald.

We normally meet in-person in the indicated room. For online editions, we use Zoom and distribute the link through the mailing list. If you wish to be put on the mailing list, please subscribe to ntag-external using lists.sfu.ca