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.
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https://hdl.handle.net/11365/37832
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