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: Description: Research/departmental seminar

Seminar usually meets in-person. For online editions, the Zoom link is shared via mailing list.