応用特異点論ラボ・セミナー：Projections of surfaces in P^3：Joachim Rieger (Martin Luther University Halle-Wittenberg)

開催日時

2018年12月13日 16時30分 ～ 2018年12月13日 18時00分

場所

北海道大学・理学部３号館 ３－２１０室

講演者

Joachim Rieger (Martin Luther University Halle-Wittenberg)

Title: Projections of surfaces in P^3

Abstract:
For an open and dense set PG of real smooth surfaces M in real projective 3-space P^3, the family of projections from points c in P^3 has C^0-versally unfolded multi-singularities belonging to a finite list of equivalence classes (despite the appearance of certain uni-modal multi-singularities in our classification).

The stratification of M by equisingularity classes of inner projections (from points c of M) includes certain (most?) curves and points of interest in the generic geometry of surfaces as strata, and hence provides local models for the neighborhoods of such curves and points in M.

A fairly complete picture of the enumerative geometry of complex algebraic surfaces and their view bifurcation sets can be obtained for a constructible set PGC (the complex analogue of PG) of “generic degree of surfaces” from an old result of H. Schubert. In fact, H. Schubert used the term “Allgemeine Ordnungsflache” (general degree of surface) without defining it.