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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
We cover, in this way, a range of (d, g, n) outside the Brill–Noether range.
📌 3 Key Takeaways
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Objective & Hypothesis:For all integers n, d, g such 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 P n with degree d and genus g .
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Key Findings & Data:For most of these (d, g), we prove that a general X ∈ A(d, g; n) has maximal rank.
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Conclusion & Impact:We cover, in this way, a range of (d, g, n) outside the Brill–Noether range.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
For all integers n, d, g such 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 P n with degree d and 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.
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Cite This Article
BALLICO, E. (2022). Good components of curves in projective spaces outside the Brill–Noether range. Turkish Journal of Mathematics, Cilt: 45 - Sayı: 1, 423–444. https://ajindex.com/articles/607343