On the gonality sequence of an algebraic curve

الأصل · EN

For any smooth irreducible projective curve X, the gonality sequence {dᵣ | r ∈ N } is a strictly increasing sequence of positive integer invariants of X. In most known cases dᵣ₊₁ is not much bigger than dᵣ. In our terminology this means the numbers dᵣ satisfy the slope inequality. It is the aim of this paper to study cases when this is not true. We give examples for this of extremal curves in ʳ, for curves on a general K3-surface in ʳ and for complete intersections in ³.