31 research outputs found
Hilbert scheme of linearly normal curves in with index of speciality five and beyond
We study the Hilbert scheme of smooth, irreducible, non-degenerate and
linearly normal curves of degree and genus in ()
whose complete and very ample hyperplane linear series have
relatively small index of speciality . In particular we
determine the existence as well as the non-existence of Hilbert schemes of
linearly normal curves for every possible
triples with and . We also determine the
irreducibility of the Hilbert scheme
when the genus is near to the minimal possible value with respect to the
dimension of the projective space for which
, say .
In the course of proofs of key results, we show the existence of linearly
normal curves of degree with arbitrarily given index of speciality
with some mild restriction on the genus .Comment: 60 pages, added two figures illustrating main results and corrected
typo
On the Hilbert scheme of linearly normal curves in with small index of speciality
We study the Hilbert scheme of smooth, irreducible, non-degenerate and
linearly normal curves of degree and genus in whose
complete and very ample hyperplane linear series have relatively
small index of speciality . In particular we show the
existence and the non-existence of certain Hilbert schemes with
. We also determine the irreducibility of
for , which are rather
peculiar families in some sense.Comment: 25 pages. Comments are very welcome. arXiv admin note: text overlap
with arXiv:2101.0055
On the Hilbert scheme of smooth curves of degree and genus in
We denote by the Hilbert scheme of smooth curves, which
is the union of components whose general point corresponds to a smooth
irreducible and non-degenerate curve of degree and genus in
. In this article, we show that is non
empty and reducible with two components of the expected dimension hence
generically reduced. We also study the birationality of the moduli map up to
projective motion and several key properties such as gonality of a general
element as well as specifying smooth elements of each components.Comment: Final version; corrected many typos in the exposition. To appear in
Bollettino dell'Unione Matematica Italian
On the Hilbert scheme of smooth curves of degree in
We denote by the Hilbert scheme of smooth curves, which
is the union of components whose general point corresponds to a smooth
irreducible and non-degenerate curve of degree and genus in
. In this article, we study for every
possible genus and determine their irreducibility. We also study the
birationality of the moduli map up to projective equivalence and several key
properties such as gonality of a general element as well as characterizing
smooth elements of each component.Comment: Incorrect statement in Remark 3.8 has been corrected. Several typos
has been fixe