George H. Hitching

activity

20242026

collaborators

5 papers

math.AG2026

Stability of kernel bundles on projective bundles over curves

Abel Castorena, George H. Hitching

Let $X$ be a projective bundle over a smooth curve $C$ of genus $g \geq 3$ , and consider the relative hyperplane bundle $O_{X} (1) \to X$ . Let $V \subseteq H^0 ( X , {\math…

math.AG2026

Segre invariants of principal bundles over a curve

George H. Hitching, Alfonso Zamora

For a vector bundle $V$ over a curve $X$ , the Segre invariant $s_{n} (V)$ encodes the maximal degree attained by rank $n$ subbundles of $V$ . The functions $s_{n}$ define stratification…

math.AG2025

Geometry of linearly stable coherent systems over curves

Abel Castorena, George H. Hitching

Let $E$ be a vector bundle over a smooth curve $C$ , and $V$ a generating space of sections of $E$ . We characterise Mumford linear stability of the associated projective model of $\…

math.AG2025

On Î±-stability and linear stability of generated coherent systems

Abel Castorena, George H. Hitching

There is a well studied notion of GIT-stability for coherent systems over curves, which depends on a real parameter $I^\pm$ . For generated coherent systems, there is a further notion…

math.AG2024

Martens and Mumford theorems for higher rank Brill--Noether loci

Parviz Asefi Nazarlou, Ali Bajravani, George H. Hitching

Generalizing the Martens theorem for line bundles over a curve $C$ , we obtain upper bounds on the dimension of the Brill--Noether locus $B_{n, d}^{k}$ parametrizing stable bundles of…