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Non-obstructed subcanonical space curves.

Rosa M. Miró-Roig (1992)

Publicacions Matemàtiques

Recall that a closed subscheme X ⊂ P is non-obstructed if the corresponding point x of the Hilbert scheme Hilbp(t)n is non-singular. A geometric characterization of non-obstructedness is not known even for smooth space curves. The goal of this work is to prove that subcanonical k-Buchsbaum, k ≤ 2, space curves are non-obstructed. As a main tool we use Serre's correspondence between subcanonical curves and vector bundles.

Number of singular points of an annulus in 2

Maciej Borodzik, Henryk Zołądek (2011)

Annales de l’institut Fourier

Using BMY inequality and a Milnor number bound we prove that any algebraic annulus * in 2 with no self-intersections can have at most three cuspidal singularities.

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