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| Ininitely near points: a differential approach |
| Abstract: Recently, various authors have shown
a renewed interest towards a tower of projective bundles over a nonsingular
algebraic or analytic basis, which was introduced by Semple in 1954. This
construction provides a natural framework to deal with iterated Nash transforms
of a given reduced curve in the variety basis of the tower. The underlying
algebra is higher differential calculus. I will mainly discuss the behavior
of plane curve singularities. |