Gromov–Witten theory with maximal contacts

We propose an intersection-theoretic method to reduce questions in genus zero logarithmic Gromov-Witten theory the of smooth pairs, presence positivity. The is applied enumerative geometry rational curves with maximal contact orders along a simple normal crossings divisor and recent about its relationship local curve counting. Three results are established. produce counterexamples local/logarithmic conjectures van Garrel-Graber-Ruddat Tseng-You. prove that weak form conjecture holds for product geometries. Finally, we explicitly determine difference between theories, terms relative invariants which efficient algorithms known. polyhedral tropical moduli maps plays essential intricate role analysis.