Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4668788 | Bulletin des Sciences Mathématiques | 2015 | 69 Pages |
Abstract
In this paper we obtain an explicit formula for the number of curves in P2P2, of degree d , passing through (d(d+3)/2−(k+1))(d(d+3)/2−(k+1)) generic points and having one node and one codimension k singularity, where k is at most 6. Our main tool is a classical fact from differential topology: the number of zeros of a generic smooth section of a vector bundle V over M, counted with a sign, is the Euler class of V evaluated on the fundamental class of M.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Somnath Basu, Ritwik Mukherjee,