Enumeration Of Rational Plane Curves Tangent To A Smooth Cubic

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Advances In Mathematics


We compute the number of rational degree d plane curves having prescribed fixed and moving contacts to a smooth plane cubic E . We use twisted stable maps to the stack View the MathML sourceP²_E,r for r large, where View the MathML sourceP²_E,r is the r th root of P² along E. We prove that certain Gromov–Witten invariants of this stack are enumerative, and establish recursive formulas for these numbers.