We show some non-emptiness results for the Severi varieties of nodal curves with fixed geometric genus in Pn, n > 2. For n = 3, we also fix a vector bundle E of rank 2 and look at the variety Vδ(E) parameterizing sections of E whose 0-locus is nodal, with fixed geometric genus. We establish some basic facts about Vδ(E) and prove some (almost sharp) non-obstructedness results for these varieties.

Ballico, E., Chiantini, L. (1998). A look into the Severi varieties of curves in higher codimension. COLLECTANEA MATHEMATICA, 49(2-3), 191-201.

A look into the Severi varieties of curves in higher codimension.

CHIANTINI, LUCA
1998-01-01

Abstract

We show some non-emptiness results for the Severi varieties of nodal curves with fixed geometric genus in Pn, n > 2. For n = 3, we also fix a vector bundle E of rank 2 and look at the variety Vδ(E) parameterizing sections of E whose 0-locus is nodal, with fixed geometric genus. We establish some basic facts about Vδ(E) and prove some (almost sharp) non-obstructedness results for these varieties.
Ballico, E., Chiantini, L. (1998). A look into the Severi varieties of curves in higher codimension. COLLECTANEA MATHEMATICA, 49(2-3), 191-201.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/37832
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