Abstract
We prove that the moduli space of contact stable maps to P2n+1 of degree d admits a stratification parameterized by graphs. We use it to determine the number of irreducible rational contact curves in P2n+1 with any Schubert condition. We give explicitely some of these invariants for P3 and P5. We give another proof of the formula for the number of plane contact curves in P3 meeting the appropriate number of lines.
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