Higher-dimensional analogues of stable curves

Details Higher-dimensional analogues of stable curves Higher-dimensional analogues of stable curves

2006-07-26

arxiv.org/abs/math/0607682v1

Proceedings of Madrid ICM2006, European Math. Soc. Publ. House

Mathematics

Algebraic Geometry

Scientific paper

The Minimal Model Program offers natural higher-dimensional analogues of stable $n$-pointed curves and maps: stable pairs consisting of a projective variety $X$ of dimension $\ge2$ and a divisor $B$, that should satisfy a few simple conditions, and stable maps $f:(X,B)\to Y$. Although MMP remains conjectural in higher dimensions, in several important situations the moduli spaces of stable pairs, generalizing those of Deligne-Mumford, Knudsen and Kontsevich, can be constructed more directly, and in considerable generality. We review these constructions, with particular attention paid to varieties with group action, and list some open problems.

Affiliated with

Also associated with

No associations

Rating

Higher-dimensional analogues of stable curves 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 Higher-dimensional analogues of stable curves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Higher-dimensional analogues of stable curves will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-478648