22 research outputs found
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 -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 -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 -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