Holomorphic vector bundles on primary Kodaira surfaces

It is in general unknown which topological complex vector bundles on a non-algebraic surface admit holomorphic structures. We solve this problem for primary Kodaira surfaces by using results of Kani on curves of genus two with elliptic differentials. Some of the corresponding moduli spaces will be smooth compact and holomorphically symplectic.Comment: 10 pages, late

Relating Catlin and D'Angelo qq-types

We clarify the relationship between the two most standard measurements of the order of contact of q-dimensional complex varieties with a real hypersurface, the Catlin and D'Angelo $q$-types, by showing that the former equals the generic value of the normalized order of contact measured along curves whose infimum is by definition the D'Angelo $q$-type.Comment: 11 pages. arXiv admin note: text overlap with arXiv:1302.229

On the Relationship between D'Angelo q-type and Catlin q-type

We establish inequalities relating two measurements of the order of contact of q-dimensional complex varieties with a real hypersurface.Comment: 18 pages; accepted at the Journal of Geometric Analysis; see arXiv:1102.0356 for the origin of this investigatio

Generalized complex structures on Kodaira surfaces

We compute the deformations in the sense of generalized complex structures of the standard classical complex structure on a primary Kodaira surface and we prove that the obtained family of deformations is a smooth locally complete family depending on four complex parameters. This family is the same as the extended deformations (in the sense of Kontsevich and Barannikov) in degree two, obtained by Poon using differential Gerstenhaber algebras

Algebraic Complete Integrability of the Bloch-Iserles System

The goal of this paper is the proof of the algebraic complete integrability of the Bloch-Iserles Hamiltonian system [5]. This result was conjectured in [4], based on its validity in certain special cases