For all integers n,d,gsuch that n≥4, d≥n+ 1, and (n+ 2)(d−n−1) ≥n(g−1), we define a good (i.e. generically smooth of dimension (n+ 1)d+ (3 −n)(g−1) and with the expected number of moduli) irreducible component A(d,g; n) of the Hilbert scheme of smooth and nondegenerate curves in Pnwith degree dand genus g. For most of these (d,g), we prove that a general X∈A(d,g; n) has maximal rank. We cover, in this way, a range of (d,g,n) outside the Brill–Noether range.

Good components of curves in projective spaces outside the Brill-Noether range / Ballico, Edoardo. - In: TURKISH JOURNAL OF MATHEMATICS. - ISSN 1303-6149. - ELETTRONICO. - 2021, 45:(2021), pp. 423-444. [10.3906/mat-1911-106]

Good components of curves in projective spaces outside the Brill-Noether range

Ballico, Edoardo
2021-01-01

Abstract

For all integers n,d,gsuch that n≥4, d≥n+ 1, and (n+ 2)(d−n−1) ≥n(g−1), we define a good (i.e. generically smooth of dimension (n+ 1)d+ (3 −n)(g−1) and with the expected number of moduli) irreducible component A(d,g; n) of the Hilbert scheme of smooth and nondegenerate curves in Pnwith degree dand genus g. For most of these (d,g), we prove that a general X∈A(d,g; n) has maximal rank. We cover, in this way, a range of (d,g,n) outside the Brill–Noether range.
2021
Ballico, Edoardo
Good components of curves in projective spaces outside the Brill-Noether range / Ballico, Edoardo. - In: TURKISH JOURNAL OF MATHEMATICS. - ISSN 1303-6149. - ELETTRONICO. - 2021, 45:(2021), pp. 423-444. [10.3906/mat-1911-106]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/308503
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