13 research outputs found
Integral cohomology of the Generalized Kummer fourfold
We describe the integral cohomology of the Generalized Kummer fourfold giving
an explicit basis, using Hilbert scheme cohomology and tools developed by
Hassett and Tschinkel. Then we apply our results to a IHS variety with
singularities, obtained by a partial resolution of the Generalized Kummer
quotiented by a symplectic involution. We calculate the Beauville--Bogomolov
form of this new variety, presenting the first example of such a form that is
odd.Comment: 40 pages, to appear in Algebraic Geometr
Integral cohomology of quotients via toric geometry
We describe the integral cohomology of a compact complex manifold
quotiented by a cyclic group of prime order with only isolated fixed
points. As a preliminary step, we investigate the integral cohomology of toric
blow-ups of quotients of . We also provide necessary and
sufficient conditions for having the spectral sequence of equivariant
cohomology of degenerated at the second page. As an application, we
compute the Beauville--Bogomolov form of Hilbert schemes of points on a K3
surface quotiented by automorphisms of orders 5 and 7.Comment: 32 page
Construction of G_2-instantons via twisted connected sums
We propose a method to construct G_2-instantons over a compact twisted
connected sum G_2-manifold, applying a gluing result of S\'a Earp and Walpuski
to instantons over a pair of 7-manifolds with a tubular end (see
arXiv:1310.7933). In our example, the moduli spaces of the ingredient
instantons are non-trivial, and their images in the moduli space over the
asymptotic cross-section K3 surface intersect transversely. Such a pair of
asymptotically stable holomorphic bundles is obtained using a twisted version
of the Hartshorne-Serre construction, which can be adapted to produce other
examples. Moreover, their deformation theory and asymptotic behaviour are
explicitly understood, results which may be of independent interest.Comment: 22 pages. Final version to appear in Mathematical Research Letter