Lefschetz pencils and divisors in moduli space
By I. Smith. 2000
53 citations recorded by the source corpus.
We study Lefschetz pencils on symplectic four-manifolds via the associated spheres in the moduli spaces of curves, and in particular their intersections with certain natural divisors. An invariant defined from such intersection numbers can distinguish manifolds with torsion first Chern class. We prove that pencils of large degree always give spheres which behave `homologically' like rational curves; contrastingly, we give the first constructive example of a symplectic non-holomorphic Lefschetz pencil. We also prove that only finitely many values of signature or Euler characteristic are realised by manifolds admitting Lefschetz pencils of genus two curves.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/6647c5811652fac4d253b283a19045ab5fd0cd6a
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In Computational Theory and Mathematics
In Geometry and Topology
- I. Smith
- Seiji Nagami
- Simon Donaldson
- H. Endo
- G'abor Sz'ekelyhidi
- Chi Li
- Robert J. Berman
- Xiuxiong Chen
In Mathematical Physics
Citations in the corpus
- Holomorphic triangle invariants and the topology of symplectic four-manifolds (2002, unknown): “ar X iv :m at h/ 02 01 04 9v 1 [ m at h. SG ] 8 J an 2 00”
- Lefschetz pencils and the canonical class for symplectic four-manifolds (2000, methodology): “One route to proving this is by stabilisation, as in [Smi01] ; it also follows from the formulae of Auroux and Katzarkov [AK].”
- Signature of relations in mapping class groups and non-holomorphic Lefschetz fibrations (2004, background): “If g ≥ 1, (II) and (III) can be replaced by (IV) all the star relators E. Luo [26] improved Gervais’ infinite presentation to show that all the relators were essentially discovered by Dehn.”