Plucker relations for space curves
Terry Wall (University of Liverpool)
Monday 8th March, 2010 16:00-17:00 Mathematics Building, room 204
The classical relations of Plucker between the invariants and singularities of a plane curve can be expressed as two linear relations and two involving quadratic terms. The linear relations were generalised to curves in n-space already in the 19th century, but true generalisations of the others were obtained only in 3-space. I will show how to obtain formulae in n-space for generic curves corresponding to all those in the plane. Also, using the theory of excess intersections, the formula for the number of osculating (n-2)-spaces meeting the curve again can be rewritten to apply to an arbitrary curve, giving a number which is a sum of local contributions, which can be calculated in numerous cases.