It was pointed out by D. Kaledin that the proof of Prop. 3.8 is wrong. Actually, the proposition itself cannot be true as we shall explain below. It was used to prove Cor. 3.10 and Thm. 3.11. Theâ€¦ (More)

For K3 surfaces the moduli space M consists of two connected components which can be identified by (X,Ïƒ) 7â†’ (X,âˆ’Ïƒ). The global Torelli theorem for K3 surfaces asserts that the period map P restrictedâ€¦ (More)

Compact hyperkÃ¤hler manifolds, or irreducible symplectic manifolds as they will be frequently called in these notes, are higher-dimensional analogues of K3 surfaces. That they indeed share many ofâ€¦ (More)

During the last years there has been growing interest in vector bundles with additional structures, e.g. parabolic and level structures. This paper results from an attempt to constructâ€¦ (More)

We prove that two derived equivalent twisted K3 surfaces have isomorphic periods. The converse is shown for K3 surfaces with large Picard number. It is also shown that all possible twisted derivedâ€¦ (More)

Besides abelian varieties, there are essentially two types of smooth projective variety with trivial canonical bundle, Calabiâ€“Yau and holo-morphic symplectic manifolds. They are distinguished, amongâ€¦ (More)

In symplectic geometry, it is often useful to consider the so-called Poisson bracket on the algebra of functions on a C symplectic manifold M . The bracket determines, and is determined by, theâ€¦ (More)

This article collects a few observations concerning Hitchinâ€™s generalized Calabi-Yau structures in dimension four. I became interested in these while thinking about the moduli space of K3 surfacesâ€¦ (More)

BECAUSE of the chemical inertness of alkanes, the introduction of functional groups into them by oxidation has tended to require severe and thus unselective conditions. The homogeneous andâ€¦ (More)