Burban I. I.
Ukr. Mat. Zh. - 2005. - 57, № 1. - pp. 18–31
We discuss a categorical approach to the investigation of topological D-branes. Twist functors and their induced action on the cohomology ring of a manifold are studied. A nontrivial spherical object of the derived category of coherent sheaves of a reduced plane singular curve of degree 3 is constructed.
Ukr. Mat. Zh. - 2003. - 55, № 7. - pp. 867-874
We give a classification of stable vector bundles on a rational curve with one simple double point.