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Applicant:
Indian Institute of Technology (IIT) Patna 
Author:
Rahul K. Singh, Ritwik Mukherjee, Anantadulal Paul,  
Corresponding Authors:
Ritwik Mukherjee 
DOI #:
https://doi.org/10.1016/j.bulsci.2018.10.001 
Title:
Enumeration of rational curves in a moving family of P 2 ,  
Journal:
Bulletin des Sciences Mathematiques 
Year:
2019 
Volume:
1–11 
Page:
150 
Keywords:
Enumerative geometry, Gromov–Witten invariants 
Abstract:
We obtain a recursive formula for the number of rational degree d curves in P3, whose image lies in a P2, intersecting r lines and s points, where r+2s = 3d+2. This can be viewed as a family version of the classical question of counting rational curves in P2. We verify that our numbers are consistent with those obtained by T. Laarakker, where he studies the parallel question of counting δ-nodal degree d curves in P3 whose image lies inside a P2. Our numbers give evidence to support the conjecture, that the polynomials obtained by T. Laarakker are enumerative when d ≥ 1 + [ δ 2 ], which is analogous to the Göttsche threshold for counting nodal curves in P2 
Entered by:
Venkata Dantham on 2020-08-04 
 
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