Nodal curves and Riccati solutions of Painlevé equations

Details Nodal curves and Riccati solutions of Painlevé equations Nodal curves and Riccati solutions of Painlevé equations

2002-01-23

arxiv.org/abs/math/0201225v1

J. Math. Kyoto Univ., 44(2004), no.3, 529--568

Mathematics

Algebraic Geometry

30 pages, 4 figures

Scientific paper

In this paper, we study Riccati solutions of Painlev\'e equations from a view point of geometry of Okamoto-Painlev\'e pairs $(S,Y)$. After establishing the correspondence between (rational) nodal curves on $S-Y$ and Riccati solutions, we give the complete classification of the configurations of nodal curves on $S-Y$ for each Okamoto-Painlev\'e pair $(S, Y)$. As an application of the classification, we prove the non-existence of Riccati solutions of Painlev\'e equations of types $P_{I}, P_{III}^{\tilde{D}_8}$ and $P_{III}^{\tilde{D}_7}$. We will also give a partial answer to the conjecture in (STT) and (T) that the dimension of the local cohomology $H^1_{Y_{red}}(S,\Theta_S(-\log Y_{red}))$ is one.

Affiliated with

Also associated with

No associations

Rating

Nodal curves and Riccati solutions of Painlevé equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Nodal curves and Riccati solutions of Painlevé equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nodal curves and Riccati solutions of Painlevé equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-153788