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Symplectic enumeration

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Abstract

Every complex projective space of odd dimension carries a natural contact structure. We give first steps towards the enumeration of curves in ℙ3 tangent to the contact structure. Such a curve is involutive in the sense that its homogeneous ideal is closed under Poisson bracket. Involutive curves in ℙ3 contained in a plane split as a union of concurrent lines. We give a formula for the number of plane involutive curves of a given degree in ℙ3 meeting the appropriate number of lines. We also discuss strategies to deal with the enumeration of involutive rational curves.

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Authors and Affiliations

  1. Departamento de Matemática, USP-S. Carlos, 13560-970, São Carlos, SP, Brazil

    D. Levcovitz & I. Vainsencher

Authors
  1. D. Levcovitz
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  2. I. Vainsencher
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Corresponding author

Correspondence to I. Vainsencher.

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Partially supported by CNPq-Brasil.

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Levcovitz, D., Vainsencher, I. Symplectic enumeration. Bull Braz Math Soc, New Series 42, 347–358 (2011). https://doi.org/10.1007/s00574-011-0019-2

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  • DOI: https://doi.org/10.1007/s00574-011-0019-2

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