Weierstrass polynomials and plane pseudo-holomorphic curves

Bernd Siebert, Gang Tian

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


For an almost complex structure J on U ⊂ ℝ4 pseudo-holomorphically fibered over ℂ a J-holomorphic curve C ⊂ U can be described by a Weierstrass polynomial. The J-holomorphicity equation descends to a perturbed ∂̄-operator on the coefficients; the operator is typically (0, 2/m)-Hölder continuous if m is the local degree of C over ℂ. This sheds some light on the problem of parametrizing pseudo-holomorphic deformations of J-holomorphic curve singularities.

Original languageEnglish (US)
Pages (from-to)1-10
Number of pages10
JournalChinese Annals of Mathematics. Series B
Issue number1
StatePublished - 2002

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


  • Plane pseudo-holomorphic curves
  • Weierstrass polynomials


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