De Jonquières’ formula for a family of nodal curves

2016 ◽  
Vol 26 (08) ◽  
pp. 1503-1528
Author(s):  
Kwangwoo Lee
Keyword(s):  
Linear System ◽  
Parameter Family ◽  
Nodal Curves ◽  
Number Of Divisors ◽  
Single Curve

For a given linear system on a curve, the number of divisors of a certain type contained in this system is known as the formula of de Jonquières. In this paper, we give an algorithm for getting a general de Jonquières formula for a family of nodal curves. Using this algorithm we obtain one of such formulas for a particular case; on a single partition [Formula: see text] of [Formula: see text] for a one parameter family of nodal curves. Moreover we retrieve the classical de Jonquières’ formula for a single curve using the method developed in this paper.

scholarly journals THE DI FRANCESCO–ITZYKSON–GÖTTSCHE CONJECTURES FOR NODE POLYNOMIALS OF ℙ2

2012 ◽  
Vol 23 (04) ◽  
pp. 1250049 ◽  
Author(s):  
NIKOLAY QVILLER
Keyword(s):  
Linear System ◽  
Line Bundle ◽  
Projective Surface ◽  
Universal Functions ◽  
Recursive Procedure ◽  
Bell Polynomial ◽  
Nodal Curves ◽  
Chern Numbers ◽  
Classical Shape ◽  
Linear Polynomials

For a smooth, irreducible projective surface S over ℂ, the number of r-nodal curves in an ample linear system [Formula: see text] (where [Formula: see text] is a line bundle on S) can be expressed using the rth Bell polynomial Pr in universal functions ai, 1 ≤ i ≤ r, of (S, [Formula: see text]), which are ℤ-linear polynomials in the four Chern numbers of S and [Formula: see text]. We use this result to establish a proof of the classical shape conjectures of Di Francesco–Itzykson and Göttsche governing node polynomials in the case of ℙ2. We also give a recursive procedure which provides the [Formula: see text]-term of the polynomials ai.

Chaos in a manifold piecewise linear system

1981 ◽  
Vol 64 (10) ◽  
pp. 9-17 ◽  
Author(s):  
Toshimichi Saito ◽  
Hiroichi Fujita
Keyword(s):  
Linear System ◽  
Piecewise Linear ◽  
Piecewise Linear System

Impossibility of steady squeezing for two-mode linear system without self-action

1991 ◽  
Vol 1 (9) ◽  
pp. 1217-1227 ◽  
Author(s):  
A. A. Bakasov ◽  
N. V. Bakasova ◽  
E. K. Bashkirov ◽  
V. Chmielowski
Keyword(s):  
Linear System
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