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Symplectic involutions on deformations of K3[2]

Giovanni Mongardi (2012)

Open Mathematics

Let X be a hyperkähler manifold deformation equivalent to the Hilbert square of a K3 surface and let φ be an involution preserving the symplectic form. We prove that the fixed locus of φ consists of 28 isolated points and one K3 surface, and moreover that the anti-invariant lattice of the induced involution on H 2(X, ℤ) is isomorphic to E 8(−2). Finally we show that any couple consisting of one such manifold and a symplectic involution on it can be deformed into a couple consisting of the Hilbert...

Symplectic structures on moduli spaces of framed sheaves on surfaces

Francesco Sala (2012)

Open Mathematics

We provide generalizations of the notions of Atiyah class and Kodaira-Spencer map to the case of framed sheaves. Moreover, we construct closed two-forms on the moduli spaces of framed sheaves on surfaces. As an application, we define a symplectic structure on the moduli spaces of framed sheaves on some birationally ruled surfaces.

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