18,577 research outputs found
Second fundamental form of the Prym map in the ramified case
In this paper we study the second fundamental form of the Prym map in the ramified case .
We give an expression of it in terms of the second fundamental form of the
Torelli map of the covering curves. We use this expression to give an upper
bound for the dimension of a germ of a totally geodesic submanifold, and hence
of a Shimura subvariety of , contained in the
Prym locus.Comment: To appear in Galois Covers, Grothendieck-Teichmueller Theory and
Dessins d'Enfants - Interactions between Geometry, Topology, Number Theory
and Algebra. Springer Proceedings in Mathematics & Statistics. arXiv admin
note: text overlap with arXiv:1711.0342
On totally geodesic submanifolds in the Jacobian locus
We study submanifolds of A_g that are totally geodesic for the locally
symmetric metric and which are contained in the closure of the Jacobian locus
but not in its boundary. In the first section we recall a formula for the
second fundamental form of the period map due to Pirola, Tortora and the first
author. We show that this result can be stated quite neatly using a line bundle
over the product of the curve with itself. We give an upper bound for the
dimension of a germ of a totally geodesic submanifold passing through [C] in
M_g in terms of the gonality of C. This yields an upper bound for the dimension
of a germ of a totally geodesic submanifold contained in the Jacobian locus,
which only depends on the genus. We also study the submanifolds of A_g obtained
from cyclic covers of the projective line. These have been studied by various
authors. Moonen determined which of them are Shimura varieties using deep
results in positive characteristic. Using our methods we show that many of the
submanifolds which are not Shimura varieties are not even totally geodesic.Comment: To appear on International Journal of Mathematic
Single-species fragmentation: the role of density-dependent feedbacks
Internal feedbacks are commonly present in biological populations and can
play a crucial role in the emergence of collective behavior. We consider a
generalization of Fisher-KPP equation to describe the temporal evolution of the
distribution of a single-species population. This equation includes the
elementary processes of random motion, reproduction and, importantly, nonlocal
interspecific competition, which introduces a spatial scale of interaction.
Furthermore, we take into account feedback mechanisms in diffusion and growth
processes, mimicked through density-dependencies controlled by exponents
and , respectively. These feedbacks include, for instance, anomalous
diffusion, reaction to overcrowding or to rarefaction of the population, as
well as Allee-like effects. We report that, depending on the dynamics in place,
the population can self-organize splitting into disconnected sub-populations,
in the absence of environment constraints. Through extensive numerical
simulations, we investigate the temporal evolution and stationary features of
the population distribution in the one-dimensional case. We discuss the crucial
role that density-dependency has on pattern formation, particularly on
fragmentation, which can bring important consequences to processes such as
epidemic spread and speciation
Shimura varieties in the Torelli locus via Galois coverings of elliptic curves
We study Shimura subvarieties of obtained from families of
Galois coverings where is a smooth complex
projective curve of genus and . We give the complete list
of all such families that satisfy a simple sufficient condition that ensures
that the closure of the image of the family via the Torelli map yields a
Shimura subvariety of for and for all and
for and . In a previous work of the first and second author
together with A. Ghigi [FGP] similar computations were done in the case .
Here we find 6 families of Galois coverings, all with and
and we show that these are the only families with satisfying this
sufficient condition. We show that among these examples two families yield new
Shimura subvarieties of , while the other examples arise from
certain Shimura subvarieties of already obtained as families of
Galois coverings of in [FGP]. Finally we prove that if a family
satisfies this sufficient condition with , then .Comment: 18 pages, to appear in Geometriae Dedicat
Satellite To Satellite Doppler Tracking (SSDT) for mapping of the Earth's gravity field
Two SSDT schemes were evaluated: a standard, low-low, SSDT configuration, which both satellites are in basically the same low altitude nearly circular orbit and the pair is characterized by small angular separation; and a more general configuration in which the two satellites are in arbitrary orbits, so that different configurations can be comparatively analyed. The standard low-low SSDT configuration is capable of recovering 1 deg X 1 deg surface anomalies with a strength as low as 1 milligal, located on the projected satellite path, when observing from a height as large as 300 km. The Colombo scheme provides an important complement of SSDT observations, inasmuch as it is sensitive to radial velocity components, while keeping at the same performance level both measuring sensitivity and measurement resolution
On the first Gaussian map for Prym-canonical line bundles
We prove by degeneration to Prym-canonical binary curves that the first
Gaussian map of the Prym canonical line bundle is
surjective for the general point [C,A] of R_g if g >11, while it is injective
if g < 12.Comment: To appear in Geometriae Dedicata. arXiv admin note: text overlap with
arXiv:1105.447
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