54,490 research outputs found
Matrix Model Maps and Reconstruction of AdS SUGRA Interactions
We consider the question of reconstructing (cubic) SUGRA interactions in
AdS/CFT. The method we introduce is based on the matrix model maps (MMP) which
were previously successfully employed at the linearized level. The strategy is
to start with the map for 1/2 BPS configurations which is exactly known (to all
orders) in the hamiltonian framework. We then use the extension of the matrix
model map with the corresponding Ward identities to completely specify the
interaction. A central point in this construction is the non-vanishing of
off-shell interactions (even for highest-weight states).Comment: 28 page
Elliptic curve configurations on Fano surfaces
The elliptic curves on a surface of general type constitute an obstruction
for the cotangent sheaf to be ample. In this paper, we give the classification
of the configurations of the elliptic curves on the Fano surface of a smooth
cubic threefold. That means that we give the number of such curves, their
intersections and a plane model. This classification is linked to the
classification of the automorphism groups of theses surfaces.Comment: 17 pages, accepted and shortened version, the rest will appear in
"Fano surfaces with 12 or 30 elliptic curves
The Schottky problem in genus five
In this paper, we present a solution to the Schottky problem in the spirit of
Schottky and Jung for genus five curves. To do so, we exploit natural incidence
structures on the fibers of several maps to reduce all questions to statements
about the Prym map for genus six curves. This allows us to find all components
of the big Schottky locus and thus, to show that the small Schottky locus
introduced by Donagi is irreducible.Comment: 20 page
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