Counting Curves with Tangencies

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2025
• Main Authors: Biswas, Indranil, Choudhury, Apratim, Mukherjee, Ritwik, Paul, Anantadulal
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2025
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212879
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Counting Curves with Tangencies. Indranil Biswas, Apratim Choudhury, Ritwik Mukherjee and Anantadulal Paul. SIGMA 21 (2025), 012, 50 pages

Interpreting tangency as a limit of two transverse intersections, we obtain a concrete formula to enumerate smooth degree plane curves tangent to a given line at multiple points with arbitrary order of tangency. Extending that idea, we then enumerate curves with one node with multiple tangencies to...