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Periodic integrals and tautological systems

Bong H. Lian, Ruifang Song, Shing-Tung Yau (2013)

Journal of the European Mathematical Society

We study period integrals of CY hypersurfaces in a partial flag variety. We construct a regular holonomic system of differential equations which govern the period integrals. By means of representation theory, a set of generators of the system can be described explicitly. The results are also generalized to CY complete intersections. The construction of these new systems of differential equations has lead us to the notion of a tautological system.

Perturbations of the metric in Seiberg-Witten equations

Luca Scala (2011)

Annales de l’institut Fourier

Let M a compact connected oriented 4-manifold. We study the space Ξ of Spin c -structures of fixed fundamental class, as an infinite dimensional principal bundle on the manifold of riemannian metrics on M . In order to study perturbations of the metric in Seiberg-Witten equations, we study the transversality of universal equations, parametrized with all Spin c -structures  Ξ . We prove that, on a complex Kähler surface, for an hermitian metric h sufficiently close to the original Kähler metric, the moduli space...

Plane curve singularities and carousels

Lê Dung Tráng (2003)

Annales de l’institut Fourier

In this paper we give a direct and explicit description of the local topological embedding of a plane curve singularity using the Puiseux expansions of its branches in a given set of coordinates.

Pluricanonical maps for threefolds of general type

Gueorgui Tomov Todorov (2007)

Annales de l’institut Fourier

In this paper we will prove that for a threefold of general type and large volume the second plurigenera is positive and the fifth canonical map is birational.

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