P1 x P2 x Fl(1,3,5) – Fano fourfolds

Ambient: ℙ¹P1 × ℙ²P2 × Fl(1, 3, 5) `12044`

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

family	bundle	$\mathrm{h}^{1,1}$	$\mathrm{h}^{1,2}$	$\mathrm{h}^{2,2}$	$\mathrm{h}^0(X, \omega_X^\vee)$	$\operatorname{vol}(X) = \mathrm{c}_1^4$	$\chi(X, \mathrm{T}_X)$
3-352-75-a	$E^{ω_{7}} \oplus E^{ω_{3} + ω_{7}} \oplus E^{ω_{1} + ω_{4}}$ E^(w7) + E^(w3 + w7) + E^(w1 + w4)	3	0	5	75	352	8
4-310-67-a	$E^{ω_{5}} \oplus E^{ω_{3} + ω_{7}} \oplus E^{ω_{1} + ω_{4}}$ E^(w5) + E^(w3 + w7) + E^(w1 + w4)	4	0	7	67	310	7
3-176-42-e	$E^{ω_{7}} \oplus E^{ω_{3} + ω_{7}} \oplus E^{ω_{1} + 2 ω_{4}}$ E^(w7) + E^(w3 + w7) + E^(w1 + 2w4)	3	1	5	42	176	-4
4-257-57-b	$(E^{ω_{4}})^{\oplus 2} \oplus E^{ω_{3} + ω_{7}} \oplus E^{ω_{1} + ω_{6}}$ 2 copies of E^(w4) + E^(w3 + w7) + E^(w1 + w6)	4	0	9	57	257	2
4-272-60-d	$E^{ω_{4}} \oplus E^{ω_{6}} \oplus E^{ω_{3} + ω_{7}} \oplus E^{ω_{1} + ω_{4}}$ E^(w4) + E^(w6) + E^(w3 + w7) + E^(w1 + w4)	4	0	7	60	272	4
4-215-49-b	$(E^{ω_{7}})^{\oplus 2} \oplus E^{ω_{2} + ω_{5}} \oplus E^{ω_{1} + ω_{4}}$ 2 copies of E^(w7) + E^(w2 + w5) + E^(w1 + w4)	4	0	9	49	215	0
5-251-56-b	$(E^{ω_{6}})^{\oplus 2} \oplus E^{ω_{7}} \oplus E^{ω_{3} + ω_{4}} \oplus E^{ω_{1} + ω_{2}}$ 2 copies of E^(w6) + E^(w7) + E^(w3 + w4) + E^(w1 + w2)	5	0	9	56	251	4