Skip to Main content Skip to Navigation
Conference papers

Relative Node Polynomials for Plane Curves

Abstract : We generalize the recent work of Fomin and Mikhalkin on polynomial formulas for Severi degrees. The degree of the Severi variety of plane curves of degree d and δ nodes is given by a polynomial in d, provided δ is fixed and d is large enough. We extend this result to generalized Severi varieties parametrizing plane curves which, in addition, satisfy tangency conditions of given orders with respect to a given line. We show that the degrees of these varieties, appropriately rescaled, are given by a combinatorially defined ``relative node polynomial'' in the tangency orders, provided the latter are large enough. We describe a method to compute these polynomials for arbitrary δ , and use it to present explicit formulas for δ ≤ 6. We also give a threshold for polynomiality, and compute the first few leading terms for any δ .
Complete list of metadata

Cited literature [17 references]  Display  Hide  Download
Contributor : Coordination Episciences Iam Connect in order to contact the contributor
Submitted on : Tuesday, October 13, 2015 - 3:06:28 PM
Last modification on : Wednesday, August 7, 2019 - 2:34:15 PM
Long-term archiving on: : Thursday, April 27, 2017 - 12:04:35 AM


Publisher files allowed on an open archive




Florian Block. Relative Node Polynomials for Plane Curves. 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.199-210, ⟨10.46298/dmtcs.2903⟩. ⟨hal-01215084⟩



Record views


Files downloads