47 research outputs found
A construction of SKT manifolds using toric geometry
No full textWe produce infinite families of SKT manifolds by using methods of toric geometry like the J-construction. These SKT manifolds are total spaces of certain principal G-bundles over smooth projective toric varieties, where G is an even dimensional compact connected Lie group
Orientation in topological K-Theory
No full textilustracionesIncluye referencias bibliográficastextocomputadorarecurso en líneaMatemáticoPregrad
Group actions, non-Kähler complex manifolds and SKT structures
No full textAbstractWe give a construction of integrable complex structures on the total space of a smooth principal bundle over a complex manifold, with an even dimensional compact Lie group as structure group, under certain conditions. This generalizes the constructions of complex structure on compact Lie groups by Samelson and Wang, and on principal torus bundles by Calabi-Eckmann and others. It also yields large classes of new examples of non-Kähler compact complex manifolds. Moreover, under suitable restrictions on the base manifold, the structure group, and characteristic classes, the total space of the principal bundle admits SKT metrics. This generalizes recent results of Grantcharov et al. We study the Picard group and the algebraic dimension of the total space in some cases. We also use a slightly generalized version of the construction to obtain (non-Kähler) complex structures on tangential frame bundles of complex orbifolds.</jats:p
BLOWDOWNS AND MCKAY CORRESPONDENCE ON FOUR DIMENSIONAL QUASITORIC ORBIFOLDS
No full textWe prove the existence of torus invariant almost complex structure on any positively omnioriented four dimensional primitive quasitoric orbifold. We construct pseudo-holomorphic blowdown maps for such orbifolds. We prove a version of McKay correspondence when the blowdowns are crepant
ALMOST COMPLEX STRUCTURE, BLOWDOWNS AND MCKAY CORRESPONDENCE IN QUASITORIC ORBIFOLDS
No full textWe prove the existence of invariant almost complex structure on any positively omnioriented quasitoric orbifold. We construct blowdowns. We define Chen--Ruan cohomology ring for any omnioriented quasitoric orbifold. We prove that the Euler characteristic of this cohomology is preserved by a crepant blowdown. We prove that the Betti numbers are also preserved if dimension is less or equal to six. In particular, our work reveals a new form of McKay correspondence for orbifold toric varieties that are not Gorenstein. We illustrate with an example
ALMOST COMPLEX STRUCTURE, BLOWDOWNS AND MCKAY CORRESPONDENCE IN QUASITORIC ORBIFOLDS
No full textWe prove the existence of invariant almost complex structure on any positively omnioriented quasitoric orbifold. We construct blowdowns. We define Chen--Ruan cohomology ring for any omnioriented quasitoric orbifold. We prove that the Euler characteristic of this cohomology is preserved by a crepant blowdown. We prove that the Betti numbers are also preserved if dimension is less or equal to six. In particular, our work reveals a new form of McKay correspondence for orbifold toric varieties that are not Gorenstein. We illustrate with an example
