P1 x P1 x P3 x P4 – Fano fourfolds

Ambient: ℙ¹P1 × ℙ¹P1 × ℙ³P3 × ℙ⁴P4 `113040`

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

family	bundle	$\mathrm{h}^{1,1}$	$\mathrm{h}^{1,2}$	$\mathrm{h}^{2,2}$	$\mathrm{h}^0(X, \omega_X^\vee)$	$\operatorname{vol}(X) = \mathrm{c}_1^4$	$\chi(X, \mathrm{T}_X)$
4-384-81-a	$E^{ω_{5} + ω_{6}} \oplus E^{ω_{2} + ω_{3}} \oplus E^{ω_{1} + ω_{3}}$ E^(w5 + w6) + E^(w2 + w3) + E^(w1 + w3)	4	0	6	81	384	12
4-187-44-a	$E^{ω_{5} + ω_{6}} \oplus E^{ω_{2} + ω_{3}} \oplus E^{ω_{1} + ω_{3} + ω_{6}}$ E^(w5 + w6) + E^(w2 + w3) + E^(w1 + w3 + w6)	4	0	14	44	187	-8
4-204-47-b	$E^{ω_{3} + ω_{6}} \oplus E^{ω_{5} + ω_{6}} \oplus E^{ω_{1} + ω_{2} + ω_{3}}$ E^(w3 + w6) + E^(w5 + w6) + E^(w1 + w2 + w3)	4	0	10	47	204	-2
4-204-47-c	$E^{ω_{4} + ω_{6}} \oplus E^{ω_{2} + ω_{6}} \oplus E^{ω_{1} + ω_{3}}$ E^(w4 + w6) + E^(w2 + w6) + E^(w1 + w3)	4	0	8	47	204	0
4-357-76-a	$E^{ω_{5} + ω_{6}} \oplus E^{ω_{2} + ω_{6}} \oplus E^{ω_{1} + ω_{3}}$ E^(w5 + w6) + E^(w2 + w6) + E^(w1 + w3)	4	0	6	76	357	10
4-199-46-a	$E^{ω_{5} + ω_{6}} \oplus E^{ω_{2} + ω_{6}} \oplus E^{ω_{1} + 2 ω_{3}}$ E^(w5 + w6) + E^(w2 + w6) + E^(w1 + 2w3)	4	1	9	46	199	-2