A few remarks about the Hilbert scheme of smooth projective curves
Edoardo Ballico, Claudio Fontanari
TL;DR
This paper examines two longstanding conjectures concerning the structure and size of the Hilbert scheme that parametrizes smooth projective curves with specified degree and genus.
Contribution
It provides insights and possibly new perspectives on Severi's and Harris's conjectures about the irreducibility and dimension of these Hilbert schemes.
Findings
Analysis of Severi's conjecture on irreducibility
Discussion of Harris's conjecture on dimension
Potential partial results or counterexamples
Abstract
We discuss two conjectures by Francesco Severi and Joe Harris about the irreducibility and the dimension of the Hilbert scheme parameterizing smooth projective curves of given degree and genus.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Advanced Algebra and Geometry