Fundamental groups of complements of plane curves and symplectic invariants
By D. Auroux, Simon Donaldson, L. Katzarkov, M. Yotov. 2002
50 citations recorded by the source corpus.
Abstract Introducing the notion of stabilized fundamental group for the complement of a branch curve in CP 2 , we define effectively computable invariants of symplectic 4-manifolds that generalize those previously introduced by Moishezon and Teicher for complex projective surfaces. Moreover, we study the structure of these invariants and formulate conjectures supported by calculations on new examples.
Subfields: Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/70b94a204b1b37a8b473d35946ec823a11fc2407
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In Geometry and Topology
- F. Catanese
- Ingrid Bauer
- L. Katzarkov
- D. Auroux
- Roberto Pignatelli
- Simon Donaldson
- Y. Odaka
- Matteo Penegini
Citations in the corpus
- Differentiable and Deformation Type of Algebraic Surfaces, Real and Symplectic Structures (2007, background): “duce invariants of symplectic structures. It seems however that, in the computations done up to now, even the groups π1(P2 C\B) allow only to detect homology invariants of the projected fourmanifold ([ADKY04]). Let us now return to the world of surfaces of general type. Suppose we have a surface Sof”
- Complex surfaces of general type: some recent progress (2006, background): “Teicher in a series of technically difficult papers ( see e.g. [MT92]). It seems however that, up to now, these groups π1(P2 C\B) allow only to detect homology invariants of the projected fourmanifold ([ADKY04]). 3) Suppose we have a surface Sof general type and a pluricanonical embedding. Then a gene”
- Luttinger surgery along Lagrangian tori and non-isotopy for singular symplectic plane curves (2002, background): “CP2, the fundamental group of the complement of the branch curve is directly related to the numerical properties of the symplectic and canonical classes. In particular, it follows from Theorem 1.5 in [3] that, if the canonical and symplectic classes are proportional to each other, then the fundament”