arXiv subjects

Matei Toma

Publications and source records attributed to Matei Toma.

40 records · Page 3Linked to original sources

arXiv2002

Holomorphic vector bundles on non-algebraic surfaces

The existence problem for holomorphic structures on vector bundles over non-algebraic surfaces is in general still open. We solve this problem in the case of rank 2 vector bundles over K3 surfaces and in the case of vector bundles of arbitrary rank over all known surfaces of class VII. Our methods, which are based on Donaldson theory and deformation theory, can be used to solve the existence problem of holomorphic vector bundles on further classes of non-algebraic surfaces.

math.AG↗

arXiv2002

Class VII surfaces with $b_2$ curves

We give an affirmative answer to a conjecture of Ma. Kato, namely that every compact complex surface $S$ in Kodaira's class $VII_0$ with $b_2(S) > 0$ and $b_2(S)$ rational curves, admits a global spherical shell.

math.CV↗

arXiv1999

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.

math.CV↗

arXiv1996

Birational models for varieties of Poncelet curves

We consider Poncelet pairs $(S,C)$, where $S$ is a smooth conic and $C$ is a degree$-c$ plane curve having the Poncelet property with respect to $S$. We prove that for $c>4$ the projection $(S,C)\mapsto C$ is generically one-to-one and use this to describe a birational model of the variety of Poncelet curves for $c$ odd.

alg-geom↗