P1 x P1 x P4 – Fano fourfolds

Ambient: ℙ¹P1 × ℙ¹P1 × ℙ⁴P4 `1140`

7 families with a presentation in this ambient variety. ← back to list

family	bundle	$\mathrm{h}^{1,1}$	$\mathrm{h}^{1,2}$	$\mathrm{h}^{1,3}$	$\mathrm{h}^{2,2}$	$\mathrm{h}^0(X, \omega_X^\vee)$	$\operatorname{vol}(X) = \mathrm{c}_1^4$	$\chi(X, \mathrm{T}_X)$
3-224-51-a	$E^{2 ω_{3}} \oplus E^{ω_{1} + ω_{2} + ω_{3}}$ E^(2w3) + E^(w1 + w2 + w3)	3	0	0	8	51	224	-3
3-64-20-a	$E^{2 ω_{3}} \oplus E^{ω_{1} + ω_{2} + 2 ω_{3}}$ E^(2w3) + E^(w1 + w2 + 2w3)	3	0	5	54	20	64	-39
3-60-19-a	$E^{3 ω_{3}} \oplus E^{ω_{1} + ω_{2} + ω_{3}}$ E^(3w3) + E^(w1 + w2 + w3)	3	5	1	22	19	60	-23
3-405-85-a	$E^{ω_{2} + ω_{3}} \oplus E^{ω_{1} + ω_{3}}$ E^(w2 + w3) + E^(w1 + w3)	3	0	0	4	85	405	12
3-208-48-c	$E^{ω_{2} + ω_{3}} \oplus E^{ω_{1} + 2 ω_{3}}$ E^(w2 + w3) + E^(w1 + 2w3)	3	0	0	12	48	208	-8
3-53-18-a	$E^{ω_{2} + ω_{3}} \oplus E^{ω_{1} + 3 ω_{3}}$ E^(w2 + w3) + E^(w1 + 3w3)	3	0	5	62	18	53	-48
3-65-20-a	$E^{ω_{2} + 2 ω_{3}} \oplus E^{ω_{1} + 2 ω_{3}}$ E^(w2 + 2w3) + E^(w1 + 2w3)	3	0	0	29	20	65	-28