J. Cobb

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math.AG2026

Weighted Syzygies of Pointed Curves

Maya Banks, John Cobb, Mahrud Sayrafi

For a point $P$ on a smooth projective curve $C$ of genus $g$ , the section ring $R_{d} = R (C, O_{C} (d P))$ can be minimally presented as a quotient $S_{d} / I_{d}$ where $S_{d}$ is a $…

math.AG2026

Inverse Eigenvalue Problems, Floquet Isospectrality and the Hilbert--Chow Morphism

John Cobb, Matthew Faust, Andreas Kretschmer

When can one change the diagonal of a matrix without changing its spectrum? We completely answer this question over an algebraically closed field of characteristic zero or larger t…

math.AG2026

Numerical Elimination: Computing Complements of Real Hypersurfaces Using Pseudo-Witness Sets

Paul Breiding, John Cobb, Aviva K. Englander +6

Many hypersurfaces in algebraic geometry, such as discriminants, arise as the projection of another variety. The real complement of such a hypersurface decomposes into connected co…