Volume 21:
Proceedings of the international conference “Geometric and Algebraic Singularity Theory” In honor of
Goo Ishikawa on the occasion of his 60th Birthday

Contents

Preface i
Editors: Osamu Saeki, Toru Ohmoto, and Wojciech Domitrz

A note on Goo Ishikawa ii
T. Ohmoto

The flat geometry of the I_1 singularity: (x,y) -> (x,xy,y^2,y^3) 1
P. Benedini Riul and R. Oset Sinha

Fronts of control-affine systems in R^3 15
Ilya Bogaevsky

Framed surfaces and one-parameter families of framed curves in Euclidean 3-space 30
Tomonori Fukunaga and Masatomo Takahashi

Jet Bundles on Gorenstein Curves and Applications 50
Letterio Gatto and Andrea T. Ricolfi

Reflexion maps and geometry of surfaces in R^4 84
Peter J. Giblin, Stanisław Janeczko, and Maria Aparecida Ruas

Equidistants for families of surfaces 97
Peter Giblin and Graham Reeve

On the Colength of Fractional Ideals 119
E. M. N. de Guzmán and A. Hefez

Duality of singularities for flat surfaces in Euclidean space 132
Atsufumi Honda

Recognition Problem of Frontal Singularities 149
Goo Ishikawa

On families of Lagrangian submanifolds 167
Shyuichi Izumiya and Masatomo Takahashi

Symmetries of special 2-flags 187
Piotr Mormul and Fernand Pelletier

Kato's chaos created by quadratic mappings associated with spherical orthotomic curves 205
Takashi Nishimura

A closedness theorem and applications in geometry of rational points over Henselian valued fields 212
Krzysztof Jan Nowak

Linking between singular locus and regular fibers 234
Osamu Saeki

Geometric algebra and singularities of ruled and developable surfaces 249
Junki Tanaka and Toru Ohmoto

Application of Singularity Theory to Bifurcation of Band Structures in Crystals 268
H. Teramoto, A. Tsuchida, K. Kondo, S. Izumiya, M. Toda, and T. Komatsuzaki

A description of a result of Deligne by log higher Albanese map 282
Sampei Usui