201 research outputs found
Abelian covers and isotrivial canonical fibrations
We classify all the surfaces of general type whose canonical map is composed
with a pencil if they are the quotient of the diagonal action by an Abelian
group acting over the product of two curves. As far as we know all the previous
examples with isotrivial canonical map are very particular cases of our
construction; moreover we find an unexpected action by a group of order 16.
This construction can be easily generalizable to all dimensions.Comment: To Appear Comm. in Al
Generalized adjoint forms on algebraic varieties
We prove a full generalization of the Castelnuovo's free pencil trick. We
show its analogies with the Adjoint Theorem; see L. Rizzi, F. Zucconi,
Differential forms and quadrics of the canonical image, arXiv:1409.1826 and
also Theorem 1.5.1 in G. P. Pirola, F. Zucconi, Variations of the Albanese
morphisms, J. Algebraic Geom. 12 (2003), no. 3, 535-572. Moreover we find a new
formulation of the Griffiths's infinitesimal Torelli Theorem for smooth
projective hypersurfaces using meromorphic -forms.Comment: 18 page
Circle of Sarkisov links on a Fano -fold
For a general Fano -fold of index in the weighted projective space
we construct new birational models that are
Mori fibre spaces, in the framework of the so-called Sarkisov program. We
highlight a relation between the corresponding birational maps, as a circle of
Sarkisov links, visualising the notion of relations (due to Kaloghiros) in
Sarkisov program
Differential forms and quadrics of the canonical image
Let be a family over a smooth connected analytic
variety , not necessarily compact, whose general fiber is smooth of
dimension , with irregularity and such that the image of the
canonical map of is not contained in any quadric of rank . We
prove that if the Albanese map of is of degree onto its image then the
fibers of are birational under the assumption that
all the -forms and all the -forms of a fiber are holomorphically liftable
to . Moreover we show that generic Torelli holds for such a family
if, in addition to the above hypothesis, we assume
that the fibers are minimal and their minimal model is unique. There are
counterexamples to the above statements if the canonical image is contained
inside quadrics of rank . We also solve the infinitesimal Torelli
problem for an -dimensional variety of general type with irregularity
and such that its cotangent sheaf is generated and the canonical map
is a rational map whose image is not contained in a quadric of rank less or
equal to .Comment: 23 pages, revised version incorporating referees' comments,
exposition improve
A note on Torelli-type theorems for Gorenstein curves
Using the notion of generalized divisors introduced by Hartshorne, we adapt
the theory of adjoint forms to the case of Gorenstein curves. We show an
infinitesimal Torelli-type theorem for vector bundles on Gorenstein curves. We
also construct explicit counterexamples to the infinitesimal Torelli claim in
the case of a reduced reducible Gorenstein curve.Comment: 17 page
- …