The Algebraic Proof of the Universality Theorem

Details The Algebraic Proof of the Universality Theorem The Algebraic Proof of the Universality Theorem

2004-02-03

arxiv.org/abs/math/0402045v1

Mathematics

Algebraic Geometry

116 pages, 8 figures

Scientific paper

In the long paper "Family Blowup formula, Admissible Graphs and the Enumeration of Singular Curves (I)" (appearing in JDG), the author solved the enumeration problem of nodal (or general singular) curve counting on algebraic surfaces by using techniques from differential topology/symplectic geometry (including family Seiberg-Witten theory) and some ideas derived from Taubes' "SW=Gr". In the current paper, we offer an algebraic proof of the "universality theorem", showing that the counting of nodal curves for 5$\delta$-1 very ample complete linear systems are controled by universal polynomials of the characteristic classes. The theorem (implicitly) was the backbone of the earlier long paper(cited above). In the current paper, we derive the result by using intersection theory and the concept of localized contributions of top Chern classes, and therefore relaxing the dependence on the symplectic techniques.

Affiliated with

Also associated with

No associations

Rating

The Algebraic Proof of the Universality Theorem 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 The Algebraic Proof of the Universality Theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Algebraic Proof of the Universality Theorem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-565414