We study the cohomology of a general stable sheaf on an abelian surface. We say that a
moduli space satisfies weak Brill-Noether if the general sheaf has at most one non-zero …

We find an algorithm to compute the cohomology groups of spherical vector bundles on
complex projective K3 surfaces, in terms of their Mukai vectors. In many good cases, we give …

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Let be a moduli space of semistable sheaves on, and let be the Brill–Noether locus of
sheaves with. In this paper, we develop the foundational properties of Brill–Noether loci on …

The Brill-Noether theory of curves plays a fundamental role in the theory of curves and their
moduli and has been intensively studied since the 19th century. In contrast, Brill-Noether …

We study tautological vector bundles over the Hilbert scheme of points on surfaces. For each
$ K $-trivial surface, we write down a simple criterion ensuring that the tautological bundles …

We provide new examples of anti-symplectic involutions on moduli spaces of stable sheaves
on K3 surfaces. These involutions are constructed through (anti) autoequivalences of the …

This thesis consists of three of my projects that are in the same direction during my PhD
study. First I develop an algorithm to compute the cohomology of stable rigid vector bundles …

0.1. Rigid vector bundles. A vector bundle is rigid if it cannot be deformed, and such
bundles, especially exceptional bundles, are fundamentally important in the studying …