Chern-Simons: Fano and Calabi-Yau

Table 2

The 18 smooth toric Fano threefolds. For full explanation of notation, see the second paragraph of Section 2.1 and those that follow.

	Id of [51]	𝐺𝑡: toric data	Geometry	(𝑏2,𝑔,𝑆𝑦𝑚)
ℙ^3	4	100−10010−10001−10	ℙ^3	(1,33,𝑈(4))
ℬ1	35	101−110011−110002−110	ℙ(𝒪ℙ^2⊕𝒪ℙ^2(2))	(2,32,[3,1^2])
ℬ2	36	100−1−10010−100001−100	ℙ(𝒪ℙ^2⊕𝒪ℙ^2(1))	(2,29,[3,1^2])
ℬ3	37	100−1−10010−1−10001−100	ℙ(𝒪ℙ^1⊕𝒪ℙ^1⊕𝒪ℙ^1(1))	(2,28,[2^2,1^2])
ℬ4	24	100−100010−1000010−10	ℙ^2×ℙ^1	(2,28,[3,2,1])
𝒞1	105	101−1010011−10100010−100	ℙ(𝒪ℙ^1×ℙ^1⊕𝒪ℙ^1×ℙ^1(1,1))	(3,27,[2^2,1^2])
𝒞2	136	100−1−1−20010−10−10001−10−10	ℙ(𝒪𝑑𝑃1⊕𝒪𝑑𝑃1(ℓ)),ℓ^2|𝑑𝑃1=1	(3,26,[2,1^3])
𝒞3	62	100−10000100−10000100−10	ℙ^1×ℙ^1×ℙ^1	(3,25,[2^3,1])
𝒞4	123	100−10−10010−10000010−100	𝑑𝑃1×ℙ^1	(3,25,[2^2,1^2])
𝒞5	68	100−1−110010−1−110001−1000	ℙ(𝒪ℙ^1×ℙ^1⊕𝒪ℙ^1×ℙ^1(1,−1))	(3,23,[2^2,1^2])
𝒟1	131	100−1−1−10010−10−10001−1000	ℙ^1-blowupofℬ2	(3,26,[2,1^3])
𝒟2	139	100−1−100010−10−10001−10−10	ℙ^1-blowupofℬ4	(3,24,[2,1^3])
ℰ1	218	100−1−10−10010−10−1−10001−10000	𝑑𝑃2bundleoverℙ^1	(4,24,[2,1^3])
ℰ2	275	100−10−1−10010−100000010−10−10	𝑑𝑃2bundleoverℙ^1	(4,23,[2,1^3])
ℰ3	266	100−10−100010−100−100010−1000	𝑑𝑃2×ℙ^1	(4,22,[2,1^3])
ℰ4	271	100−1−1−110010−10−110001−10000	𝑑𝑃2bundleoverℙ^1	(4,21,[2,1^3])
ℱ1	324	100−10−1010010−100−1100010−10000	𝑑𝑃3×ℙ^1	(5,19,[2,1^3])
ℱ2	369	100−1−10−110010−10−1−110001−100000	𝑑𝑃3bundleoverℙ^1	(5,19,[2,1^3])