2,275 research outputs found
Intersections of quadrics, moment-angle manifolds, and Hamiltonian-minimal Lagrangian embeddings
We study the topology of Hamiltonian-minimal Lagrangian submanifolds N in C^m
constructed from intersections of real quadrics in a work of the first author.
This construction is linked via an embedding criterion to the well-known
Delzant construction of Hamiltonian toric manifolds. We establish the following
topological properties of N: every N embeds as a submanifold in the
corresponding moment-angle manifold Z, and every N is the total space of two
different fibrations, one over the torus T^{m-n} with fibre a real moment-angle
manifold R, and another over a quotient of R by a finite group with fibre a
torus. These properties are used to produce new examples of Hamiltonian-minimal
Lagrangian submanifolds with quite complicated topology.Comment: 14 pages, published version (minor changes
Complete intersections: Moduli, Torelli, and good reduction
We study the arithmetic of complete intersections in projective space over
number fields. Our main results include arithmetic Torelli theorems and
versions of the Shafarevich conjecture, as proved for curves and abelian
varieties by Faltings. For example, we prove an analogue of the Shafarevich
conjecture for cubic and quartic threefolds and intersections of two quadrics.Comment: 37 pages. Typo's fixed. Expanded Section 2.
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