P1 x P2 x P2 x P4 – Fano fourfolds

Ambient: ℙ¹P1 × ℙ²P2 × ℙ²P2 × ℙ⁴P4 `1202040`

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

family	bundle	$\mathrm{h}^{1,1}$	$\mathrm{h}^{2,2}$	$\mathrm{h}^0(X, \omega_X^\vee)$	$\operatorname{vol}(X) = \mathrm{c}_1^4$	$\chi(X, \mathrm{T}_X)$
5-220-50-a	$E^{2 ω_{6}} \oplus E^{ω_{5} + ω_{6}} \oplus E^{ω_{2} + ω_{4}} \oplus E^{ω_{1} + ω_{2}}$ E^(2w6) + E^(w5 + w6) + E^(w2 + w4) + E^(w1 + w2)	5	10	50	220	2
4-203-47-a	$(E^{ω_{4} + ω_{6}})^{\oplus 2} \oplus E^{ω_{3} + ω_{6}} \oplus E^{ω_{1} + ω_{2}}$ 2 copies of E^(w4 + w6) + E^(w3 + w6) + E^(w1 + w2)	4	9	47	203	-2
4-214-49-b	$E^{ω_{4} + ω_{6}} \oplus E^{ω_{5} + ω_{6}} \oplus E^{ω_{2} + ω_{6}} \oplus E^{ω_{1} + ω_{2}}$ E^(w4 + w6) + E^(w5 + w6) + E^(w2 + w6) + E^(w1 + w2)	4	9	49	214	-1
4-209-48-a	$E^{ω_{4} + ω_{6}} \oplus E^{ω_{2} + ω_{4}} \oplus E^{ω_{3} + ω_{6}} \oplus E^{ω_{1} + ω_{6}}$ E^(w4 + w6) + E^(w2 + w4) + E^(w3 + w6) + E^(w1 + w6)	4	9	48	209	-1
4-347-74-a	$E^{ω_{5} + ω_{6}} \oplus E^{ω_{3} + ω_{6}} \oplus E^{ω_{1} + ω_{4}}$ E^(w5 + w6) + E^(w3 + w6) + E^(w1 + w4)	4	6	74	347	10
4-215-49-a	$E^{ω_{5} + ω_{6}} \oplus E^{ω_{3} + ω_{6}} \oplus E^{ω_{1} + ω_{2} + ω_{4}}$ E^(w5 + w6) + E^(w3 + w6) + E^(w1 + w2 + w4)	4	11	49	215	-2