Computational Tools for Cohomology of Toric Varieties

Table 1

Toric data for the del Pezzo-1 surface.

Vertices of the polyhedron/fan	Coords.	GLSM charges		Divisor class
		𝑄^1	𝑄^2
𝜈1=(−1,−1)	𝑥1	1	0	𝐻
𝜈2=(1,0)	𝑥2	1	0	𝐻
𝜈3=(0,1)	𝑥3	1	1	𝐻+𝑋
𝜈4=(0,−1)	𝑥4	0	1	𝑋

Intersection form: 𝐻𝑋−𝑋².
SR(𝑑𝑃₁)=⟨𝑥₁𝑥₂,𝑥₃𝑥₄⟩=⟨𝒮₁,𝒮₂⟩.