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On the structure of Brieskorn lattice

Morihiko Saito (1989)

Annales de l'institut Fourier

We study the structure of the filtered Gauss-Manin system associated to a holomorphic function with an isolated singularity, and get a basis of the Brieskorn lattice Ω X , 0 n + 1 / d f d Ω X , 0 n + 1 over { { t - 1 } } such that the action of t is expressed by t v = A 0 + A 1 t - 1 v for two matrices A 0 , A 1 with A 1 semi-simple, where v = t ( v 1 ... v μ ) is the basis. As an application, we calculate the b -function of f in the case of two variables.

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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