Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration

Abstract

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Constant Angle Ruled Surfaces with a Pointwise 1-Type Gauss Map

“…The fact that the curvatures and normal directions are important components of the vector bundle structures shows us the crucial link between the Gauss map and the geometric properties of vector bundles. Recent research on vector bundles over surfaces and curves includes the vector bundle moduli spaces over Riemann surfaces [13], the moduli space of Higgs bundles [14,15], as well as vector bundles discussed in [16,17]. The Gauss map can also visualize vector bundles' transition functions, sections, and moduli spaces, providing insights into the geometric structures of principal bundles over compact algebraic curves that were recently studied in [18].…”