N. I. Shepherd-Barron

collaborators

3 papers

math.AG2025

A non-linear differential equation for the periods of elliptic surfaces

N. I. Shepherd-Barron

Suppose that $f : X \to C$ is a general Jacobian elliptic surface over the complex numbers. Then the primitive cohomology $H_{p r im}^{1, 1} (X)$ has, up to a sign, a natural orthonormal…

math.AG2025

Recognizing flag varieties and reductive groups

I. Grojnowski, N. I. Shepherd-Barron

Fix a flat and projective morphism $X \to I^£$ of schemes. We show, first, that any set of $P^{1}$ -fibrations on $X$ defines a set of simple roots, a set of simple coro…

math.AG2024

Generic Torelli with denominators for elliptic surfaces

N. I. Shepherd-Barron

We show that a very general Jacobian elliptic surface is determined by its polarized rational Hodge structure, subject to various constraints on the irregularity and the geometric…