Geometry of families of nodal curves on rational surfaces

Mathematics – Algebraic Geometry

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

AMSLaTeX v 1.2

Scientific paper

Let P^2_r be the projective plane blown up at r generic points. Denote by E_0,E_1,...,E_r the strict transform of a generic straight line on P^2 and the exceptional divisors of the blown-up points on P^2_r respectively. We consider the variety V of all irreducible curves C in |dE_0-d_1E_1-...-d_rE_r| with k nodes as the only singularities and give asymptotically nearly optimal sufficient conditions for its smoothness, irreducibility and non-emptyness. Moreover, we extend our conditions for the smoothness and the irreducibility on families of reducible curves. For r<10 we give the complete answer concerning the existence of nodal curves in V.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Geometry of families of nodal curves on rational surfaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Geometry of families of nodal curves on rational surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geometry of families of nodal curves on rational surfaces will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-428698

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.