755 research outputs found
Genera of curves on a very general surface in
In this paper we consider the question of determining the geometric genera of
irreducible curves lying on a very general surface of degree at least 5
in (the cases are well known).
We introduce the set of all non-negative integers which are not
realized as geometric genera of irreducible curves on . We prove that
is finite and, in particular, that . The set
is the union of finitely many disjoint and separated integer
intervals. The first of them, according to a theorem of Xu, is . We show that the next one is for all .Comment: 16 page
Aging phenomena in nonlinear dissipative chains: Application to polymer
We study energy relaxation in a phenomenological model for polymer built from
rheological considerations: a one dimensional nonlinear lattice with
dissipative couplings. These couplings are well known in polymer's community to
be possibly responsible of beta-relaxation (as in Burger's model). After
thermalisation of this system, the extremities of the chain are put in contact
with a zero-temperature reservoir, showing the existence of surprising
quasi-stationary states with non zero energy when the dissipative coupling is
high. This strange behavior, due to long-lived nonlinear localized modes,
induces stretched exponential laws. Furthermore, we observe a strong dependence
on the waiting time tw after the quench of the two-time intermediate
correlation function C(tw+t,tw). This function can be scaled onto a master
curve, similar to the case of spin or Lennard-Jones glasses.Comment: 8 pages, 10 figure
Prym varieties and the canonical map of surfaces of general type
Let X be a smooth complex surface of general type such that the image of the
canonical map of X is a surface and that has degree
. Let be a desingularization of
and assume that the geometric genus of S is not zero. Beauville has
proved that in this case S is of general type and is the canonical
map of S. Beauville has also constructed the only infinite series of examples
with the above properties that was known up to now. Starting
from his construction, we define a {\em good generating pair}, namely a pair
where h is a finite morphism of surfaces and L is a nef and big
line bundle of W satisfying certain assumptions. We show that by applying a
construction analogous to Beauville's to a good generating pair one obtains an
infinite series of surfaces of general type whose canonical map is 2-to-1 onto
a canonically embedded surface. In this way we are able to construct more
infinite series of such surfaces. In addition, we show that good generating
pairs have bounded invariants and that there exist essentially only 2 examples
with . The key fact that we exploit for obtaining these results is
that the Albanese variety P of V is a Prym variety and that the fibre of the
Prym map over P has positive dimension.Comment: 40 pages, LaTeX 2.0
On the geometric genus of reducible surfaces and degenerations of surfaces to unions of planes
In this paper we study some properties of degenerations of surfaces whose
general fibre is a smooth projective surface and whose central fibre is a
reduced, connected surface , , which is assumed to be
a union of smooth projective surfaces, in particular of planes. Our original
motivation has been a series of papers of G. Zappa which appeared in the
1940-50's regarding degenerations of scrolls to unions of planes.
Here, we present a first set of results on the subject; other aspects are
still work in progress and will appear later.
We first study the geometry and the combinatorics of a surface like ,
considered as a reduced, connected surface on its own; then we focus on the
case in which X is the central fibre of a degeneration of relative dimension
two over the complex unit disk. In this case, we deduce some of the intrinsic
and extrinsic invariants of the general fibre from the ones of its central
fibre.
In the particular case of a central fibre of a semistable degeneration,
i.e. has only global normal crossing singularities and the total space of
the degeneration is smooth, some of the above invariants can be also computed
by topological methods (i.e., the Clemens-Schmid exact sequence). Our results
are more general, not only because the computations are independent on the fact
that is the central fibre of a degeneration, but also because the
degeneration is not semistable in general.Comment: latex2e, 26 pages, 11 figure
Work fluctuation theorems for harmonic oscillators
The work fluctuations of an oscillator in contact with a thermostat and
driven out of equilibrium by an external force are studied experimentally and
theoretically within the context of Fluctuation Theorems (FTs). The oscillator
dynamics is modeled by a second order Langevin equation. Both the transient and
stationary state fluctuation theorems hold and the finite time corrections are
very different from those of a first order Langevin equation. The periodic
forcing of the oscillator is also studied; it presents new and unexpected short
time convergences. Analytical expressions are given in all cases
Special scrolls whose base curve has general moduli
In this paper we study the Hilbert scheme of smooth, linearly normal, special
scrolls under suitable assumptions on degree, genus and speciality.Comment: Latex2e, shorter versio
On the classification of OADP varieties
The main purpose of this paper is to show that OADP varieties stand at an
important crossroad of various main streets in different disciplines like
projective geometry, birational geometry and algebra. This is a good reason for
studying and classifying them. Main specific results are: (a) the
classification of all OADP surfaces (regardless to their smoothness); (b) the
classification of a relevant class of normal OADP varieties of any dimension,
which includes interesting examples like lagrangian grassmannians. Following
[PR], the equivalence of the classification in (b) with the one of
quadro-quadric Cremona transformations and of complex, unitary, cubic Jordan
algebras are explained.Comment: 13 pages. Dedicated to Fabrizio Catanese on the occasion of his 60th
birthday. To appear in a special issue of Science in China Series A:
Mathematic
Fluctuation theorems for harmonic oscillators
We study experimentally the thermal fluctuations of energy input and
dissipation in a harmonic oscillator driven out of equilibrium, and search for
Fluctuation Relations. We study transient evolution from the equilibrium state,
together with non equilibrium steady states. Fluctuations Relations are
obtained experimentally for both the work and the heat, for the stationary and
transient evolutions. A Stationary State Fluctuation Theorem is verified for
the two time prescriptions of the torque. But a Transient Fluctuation Theorem
is satisfied for the work given to the system but not for the heat dissipated
by the system in the case of linear forcing. Experimental observations on the
statistical and dynamical properties of the fluctuation of the angle, we derive
analytical expressions for the probability density function of the work and the
heat. We obtain for the first time an analytic expression of the probability
density function of the heat. Agreement between experiments and our modeling is
excellent
Generalized fluctuation relation and effective temperatures in a driven fluid
By numerical simulation of a Lennard-Jones like liquid driven by a velocity
gradient \gamma we test the fluctuation relation (FR) below the (numerical)
glass transition temperature T_g. We show that, in this region, the FR deserves
to be generalized introducing a numerical factor X(T,\gamma)<1 that defines an
``effective temperature'' T_{FR}=T/X. On the same system we also measure the
effective temperature T_{eff}, as defined from the generalized
fluctuation-dissipation relation, and find a qualitative agreement between the
two different nonequilibrium temperatures.Comment: Version accepted for publication on Phys.Rev.E; major changes, 1
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