Abstract
In this paper, we give a method to describe the numerical class of a torus invariant surface on a projective toric manifold. As applications, we can classify toric 2-Fano manifolds of the Picard number 2 or of dimension at most 4.
Highlights
For a projective toric manifold X, let NE2(X) ⊂ N2(X) be the cone of numerical effective 2-cycles
As results, we obtain the classification of toric 2-Fano manifolds for the case of Picard number ρ(X) = 2 and for the case of dim(X) ≤ 4
We define a polynomial IY/X for a torus invariant subvariety Y ⊂ X. This polynomial has all the informations of intersection numbers of Y on X. We can consider this polynomial as the numerical class of Y
Summary
For a projective toric manifold X, let NE2(X) ⊂ N2(X) be the cone of numerical effective 2-cycles. For the toric case, the following is obvious: Proposition 2.4. Let Y = Yσ ⊂ X be a torus invariant subvariety of dim Y = l associated to a cone σ ∈ Σ and G(Σ) = {x1, . Xm], where Dxi is the torus invariant prime divisor corresponding to xi, while Xi is defined to be the independent variable corresponding to xi.
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