応用特異点論ラボセミナー：On the differential geometry of holomorphic plane curves (Jorge Luiz Deolindo Silva (UFSC, Brazil; Hokkaido Univ.))

開催日時

2019年11月20日 14時 45分 ～ 2019年11月20日 16時 15分

場所

北海道大学理学部 ３号館２０２

講演者

Jorge Luiz Deolindo Silva (Universidade Federal de Santa Catarina, Brazil; Hokkaido Univ.)

Title: On the differential geometry of holomorphic plane curves

Abstract:
We consider the geometry of regular holomorphic curves in \(\mathbb C^2\) viewed as surfaces in the affine space \(\mathbb R^4\). We study the \(\mathcal A\)-singularities of parallel projections of generic such surfaces along planes to transverse planes. We show that, at any point on the surface which is not an inflection point of the curve, there are two tangent directions determining two planes along which the projection have singularities of type butterfly or worse. The integral curves of these directions form a pair of foliations on the surface defined by a binary differential equation (BDE). The singularities this BDE are the inflection points of the curve together with other points that we call {\it butterfly umbilic points}. We determine the configurations of the solution curves of the BDE at its singularities.

開催場所に注意してください．

• 4限目（Jorgeさん）：3-202教室
• 5限目（早野さん）：3-204教室