Contractible classes in toric varieties

Details Contractible classes in toric varieties Contractible classes in toric varieties

2001-11-30

arxiv.org/abs/math/0111332v2

Mathematics

Algebraic Geometry

LaTeX, 27 pages, 5 figures; revised version, to appear in Mathematische Zeitschrift

Scientific paper

Let X be a smooth, complete, toric variety. We study those curves C in X that are contractible, in the sense that there exists an equivariant morphism with connected fibers, with source X, that contracts exactly the irreducible curves that are numerically equivalent to a multiple of C. When X is projective, we compare contractible and extremal curves, and we show that every curve in X is numerically equivalent to a linear combination with positive integral coefficients of contractible curves.

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