Speciality:
01.01.06 (Mathematical logic, algebra, and number theory)
Birth date:
24.12.1962
E-mail: Keywords: cycles and subschemes,
moduli spaces,
birational geometry,
algebraic vwctor bundles.
Subject:
Exceptional bundles (i.e., bundles with zero dimension moduli space) on Del Pezzo surfaces was described completely. A combinatorial structure of exceptional bundles on K3-surfaces was found. Sufficient conditions of existence of stable bundles on K3-surfaces was be formulated and proved. Using exceptional bundles as a base of derived category of coherent sheaves on Del Pezzo surfaces, it was be obtained some useful geometrical description of stable sheaves moduli spaces on the projective plane and two dimensional quadric.
Main publications:
Exceptional and rigid sheaves on surfaces with anticanonical class without base components. Algebraic geometry, 2. J. Math. Sci. (New York) 86 (1997), no. 5, 2951–3003.
Ramified coverings of $S^2$ with two degenerate branching points. Max-Planck-Institut preprint 2001 (62).
