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Enumerative invariants of stongly semipositive real symplectic six-manifolds

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arxiv math/0509121 v2 pith:47XLSWFZ submitted 2005-09-06 math.AG math.SG

Jean-Yves Welschinger (UMPA-ENSL) This is my paper · ORCID
classification math.AGmath.SG
keywords realinvariantsenumerativegivensemipositivesix-manifoldsstonglysymplectic
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abstract

Following the approach of Gromov and Witten, we define invariants under deformation of stongly semipositive real symplectic six-manifolds. These invariants provide lower bounds in real enumerative geometry, namely for the number of real rational $J$-holomorphic curves which realize a given homology class and pass through a given real configuration of points.

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Cited by 2 Pith papers

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  1. Welschinger--Witt invariants

    math.AG 2025-09 conditional novelty 8.0 of 10

    This paper builds Welschinger-Witt invariants and proves they match quadratic Gromov-Witten invariants for k-rational del Pezzo surfaces of degree at least 6, conjecturing agreement in general.

  2. A correlated refinement of the double double ramification cycle

    math.AG 2026-06 unverdicted novelty 7.0 of 10

    A Weil-pairing refinement of the DDR cycle is introduced and proved to satisfy a multiple-cover formula, yielding refined log-GW invariants of toric surfaces that also satisfy the formula.

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