911 research outputs found
Discrete invariants of varieties in positive characteristic
If is a scheme of characteristic , we define an -zip over to be
a vector bundle with two filtrations plus a collection of semi-linear
isomorphisms between the graded pieces of the filtrations. For every smooth
proper morphism satisfying certain conditions the de Rham bundles
have a natural structure of an -zip. We give a
complete classification of -zips over an algebraically closed field by
studying a semi-linear variant of a variety that appears in recent work of
Lusztig. For every -zip over our methods give a scheme-theoretic
stratification of . If the -zip is associated to an abelian scheme over
the underlying topological stratification is the Ekedahl-Oort
stratification. We conclude the paper with a discussion of several examples
such as good reductions of Shimura varieties of PEL type and K3-surfaces.Comment: 35 pages, minor changes in exposition, major changes to introductio
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
The evolution of a national research plan for computers in education in The Netherlands
This paper describes the evolution of a national research plan for computers and education in The Netherlands. This approach was initiated in 1983 and includes two phases: one from 1984 until 1988 and one from 1989 until 1992. The paper describes the research plans for the second phase, based upon the experiences of the first, and draws some general conclusions about the development of national research plans for computers in education
On some differential-geometric aspects of the Torelli map
In this note we survey recent results on the extrinsic geometry of the
Jacobian locus inside . We describe the second fundamental form
of the Torelli map as a multiplication map, recall the relation between totally
geodesic subvarieties and Hodge loci and survey various results related to
totally geodesic subvarieties and the Jacobian locus.Comment: To appear on Boll. UMI, special volume in memory of Paolo de
Bartolomei
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
On the canonical degrees of curves in varieties of general type
A widely believed conjecture predicts that curves of bounded geometric genus
lying on a variety of general type form a bounded family. One may even ask
whether the canonical degree of a curve in a variety of general type is
bounded from above by some expression , where and are
positive constants, with the possible exceptions corresponding to curves lying
in a strict closed subset (depending on and ). A theorem of Miyaoka
proves this for smooth curves in minimal surfaces, with . A conjecture
of Vojta claims in essence that any constant is possible provided one
restricts oneself to curves of bounded gonality.
We show by explicit examples coming from the theory of Shimura varieties that
in general, the constant has to be at least equal to the dimension of the
ambient variety.
We also prove the desired inequality in the case of compact Shimura
varieties.Comment: 10 pages, to appear in Geometric and Functional Analysi
Relations between some invariants of algebraic varieties in positive characteristic
We discuss relations between certain invariants of varieties in positive
characteristic, like the a-number and the height of the Artin-Mazur formal
group. We calculate the a-number for Fermat surfacesComment: 13 page
Agent Technology supports Inter-Organizational Planning in the Port
The Port of Rotterdam is a key container transshipment hub for Europe. Inland container shipping is important to connect the hinterland (40% market share). Barges visit several terminals per round-trip through the Port, thus requiring a proper planning support – to avoid planning problems such as double-bookings. A pilot version of an inter-organizational system has been build, titled APPROACH. This paper describes an industry workshop where a gamesetting was used to evaluate the current manual planning practices with the APPROACH outcome – and delivered interesting findings; both for actual implementation of the system as well as it unveiled issues for further research
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