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On the topological triviality along moduli of deformations of J k , 0 singularities

Piotr Jaworski (2000)

Annales Polonici Mathematici

It is well known that versal deformations of nonsimple singularities depend on moduli. However they can be topologically trivial along some or all of them. The first step in the investigation of this phenomenon is to determine the versal discriminant (unstable locus), which roughly speaking is the obstacle to analytic triviality. The next one is to construct continuous liftable vector fields smooth far from the versal discriminant and to integrate them. In this paper we extend the results of J....

On the variety of linear series on a singular curve

E. Ballico, C. Fontanari (2002)

Bollettino dell'Unione Matematica Italiana

Let Y be an integral projective curve with g := p a Y 2 . For all positive integers d , r let W d r Y * A * be the set of all L Pic d Y with h 0 Y , L r + 1 and L spanned. Here we prove that if d g - 2 , then dim W d r Y * A * d - 3 r except in a few cases (essentially if Y is a double covering).

On the variety of quadrics of rank four containing a projective curve

Alexis G. Zamora (1999)

Bollettino dell'Unione Matematica Italiana

Sia X P H 0 X , L * una curva proeittiva e lissa, generali nel senso di Brill-Noether, indichiamo con R 4 X l'insieme algebrico di quadrici di rango 4 contenendo a X . In questo lavoro noi descriviamo birazionalmente i componenti irriducibile di R 4 X .

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