On the projective differential geometry of plane curves and one-parameter families of conics

Conics on the Projective Plane

In this paper, we discuss a special property of conics on the projective plane and answer questions in enumerative algebraic geometry such as ”How many points determine a conic?” and ”How many conics do we expect to pass through m points and tangent to n lines?”

Conformal Geometry of One-parameter Families of Curves

A single regular analytic arc in the plane has no conformai differential invariants. The conformai theory of curvilinear angles was initiated by Kasner, and has been elaborated by him and others. The present paper is concerned with conformai differential invariants of a real one-parameter family of regular analytic arcs in the plane. We assume that the family is defined in some region R of the ...

Geometry of Families of Nodal Curves on the Blown{up Projective Plane

Let P2r be the projective plane blown up at r generic points. Denote by E0, E1, . . . , Er the strict transform of a generic straight line on P and the exceptional divisors of the blown–up points on P2r respectively. We consider the variety Virr(d; d1, . . . , dr ; k) of all irreducible curves C in |dE0 − ∑ r i=1 diEi| with k nodes as the only singularities and give asymptotically nearly optima...

the effect of explicit teaching of metacognitive vocabulary learning strategies on recall and retention of idioms

چکیده ندارد.

Representing Conics Using the Oriented Projective Plane