162 research outputs found
On a theorem of Castelnuovo and applications to moduli
In this paper we prove a theorem stated by Castelnuovo which bounds the
dimension of linear systems of plane curves in terms of two invariants, one of
which is the genus of the curves in the system. Then we classify linear systems
whose dimension belongs to certain intervals which naturally arise from
Castelnuovo's theorem. Finally we make an application to the following moduli
problem: what is the maximum number of moduli of curves of geometric genus
varying in a linear system on a surface? It turns out that, for , the
answer is , and it is attained by trigonal canonical curves varying on a
balanced rational normal scroll.Comment: 8 page
Birational classification of curves on rational surfaces
In this paper we consider the birational classification of pairs (S,L), with
S a rational surfaces and L a linear system on S. We give a classification
theorem for such pairs and we determine, for each irreducible plane curve B,
its "Cremona minimal" models, i.e. those plane curves which are equivalent to B
via a Cremona transformation, and have minimal degree under this condition.Comment: 33 page
Brill--Noether loci of stable rank--two vector bundles on a general curve
In this note we give an easy proof of the existence of generically smooth
components of the expected dimension of certain Brill--Noether loci of stable
rank 2 vector bundles on a curve with general moduli, with related applications
to Hilbert scheme of scrolls.Comment: 9 pages, submitted preprin
On Cremona contractibility of unions of lines in the plane
We discuss the concept of Cremona contractible plane curves, with an
historical account on the development of this subject. We then classify Cremona
contractible unions of d > 11 lines in the plane.Comment: 14 pages; removed section 5 which contained an incomplete proof;
accepted for publication on Kyoto Journal of Mathematic
Scrolls and hyperbolicity
Using degeneration to scrolls, we give an easy proof of non-existence of
curves of low genera on general surfaces in P3 of degree d >=5. We show, along
the same lines, boundedness of families of curves of small enough genera on
general surfaces in P3. We also show that there exist Kobayashi hyperbolic
surfaces in P3 of degree d = 7 (a result so far unknown), and give a new
construction of such surfaces of degree d = 6. Finally we provide some new
lower bounds for geometric genera of surfaces lying on general hypersurfaces of
degree 3d > 15 in P4.Comment: 17
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