Complete families of smooth space curves and strong semistability

Abstract

We construct the first non-trivial examples of complete families of non-degenerate smooth space curves, and show that the base of such a family cannot be a rational curve. Both results rely on the study of the strong semistability of certain vector bundles.

16 pages, final version

References in corpus (3)

• Semistability and Hilbert-Kunz multiplicities for curves
• On positivity and semistability of vector bundles in finite and mixed characteristics
• On the birational geometry of the parameter space for codimension 2 complete intersections