Symplectic resolutions, Lefschetz property and formality

By G. Cavalcanti, M. Fernández, V. Muñoz. 2007

48 citations recorded by the source corpus.

We introduce a method to resolve a symplectic orbifold (M, omega) into a smooth symplectic manifold ((M) over tilde,(omega) over tilde). Then we study how the formality and the Lefschetz property of ((M) over tilde,(omega) over tilde) are compared with that of (M, omega). We also study the formality of the symplectic blow-up of (M, omega) along symplectic submanifolds disjoint from the orbifold singularities. This allows us to construct the first example of a simply connected compact symplectic manifold of dimension 8 which satisfies the Lefschetz property but is not formal, therefore giving a counter-example to a conjecture of Babenko and Taimanov.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cb4312ac4643d7dcddb23f170286526bed407999

How researchers see this paper

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In Geometry and Topology

1. Adriano Tomassini
2. Anna Fino
3. L. Ugarte
4. Luigi Vezzoni
5. Valentino Tosatti

In Mathematical Physics

1. Anna Fino
2. Adriano Tomassini

Citations in the corpus

• A survey on strong KT structures (2009, background): “Theorem 3.1 can be applied to complex orbifolds endowed with a strong KT metric in a similar way as for the symplectic orbifolds (see [ 11 ]).”
• Blow-ups and resolutions of strong K\"ahler with torsion metrics (2008, methodology): “. Resolutions for quotients of tori have been already considered by Joyce in order to obtain simply-connected compact manifolds with exceptional holonomy G2 and Spin(7) in [26]. Moreover, in [13] and [9] orbifolds constructed starting with nilmanifolds have been recently used in order to get simply-”