Gianluca Pacienza

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20002005

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math.AG2005

Singular curves on a K3 surface and linear series on their normalizations

Flaminio Flamini, Andreas Leopold Knutsen, Gianluca Pacienza

In this paper, we study the Brill-Noether theory of the normalizations of singular, irreducible curves on a $K 3$ surface. We introduce a {\em singular} Brill-Noether number $ρ_{sin…

math.AG2002

Subvarieties of general type on a general projective hypersurface

Gianluca Pacienza

We study subvarieties of a general projective degree $d$ hypersurface $X_{d} \subset P^{n}$ . Our main theorem, which improves previous results of L. Ein and C. Voisin, implies i…

math.AG2000

Rational curves on general projective hypersurfaces

Gianluca Pacienza

Let $k$ be an integer such that $1 \leq k \leq n - 5$ , and $X_{2 n - 2 - k} \subset P^{n}$ a general projective hypersurface of degree $d = 2 n - 2 - k$ . In this paper we prove that the only…