P1 x Fl(1,2,5) x P2 – Fano fourfolds

Ambient: ℙ¹P1 × Fl(1, 2, 5) × ℙ²P2 `12042`

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

family	bundle	$\mathrm{h}^{1,1}$	$\mathrm{h}^{2,2}$	$\mathrm{h}^0(X, \omega_X^\vee)$	$\operatorname{vol}(X) = \mathrm{c}_1^4$	$\chi(X, \mathrm{T}_X)$
4-432-90-a	$E^{ω_{3} + ω_{7}} \oplus E^{ω_{5}} \oplus E^{ω_{1} + ω_{6}}$ E^(w3 + w7) + E^(w5) + E^(w1 + w6)	4	6	90	432	15
4-367-78-a	$E^{ω_{3} + ω_{7}} \oplus E^{ω_{5}} \oplus E^{ω_{1} + ω_{2}}$ E^(w3 + w7) + E^(w5) + E^(w1 + w2)	4	5	78	367	11
4-229-52-a	$E^{ω_{3} + ω_{7}} \oplus E^{ω_{5}} \oplus E^{ω_{1} + ω_{2} + ω_{6}}$ E^(w3 + w7) + E^(w5) + E^(w1 + w2 + w6)	4	11	52	229	-3
4-235-53-a	$E^{ω_{2} + ω_{6}} \oplus E^{ω_{3} + ω_{6}} \oplus E^{ω_{5}} \oplus E^{ω_{1} + ω_{3}}$ E^(w2 + w6) + E^(w3 + w6) + E^(w5) + E^(w1 + w3)	4	9	53	235	0
5-256-57-a	$E^{ω_{2} + ω_{6}} \oplus E^{ω_{5}} \oplus E^{2 ω_{3}} \oplus E^{ω_{1} + ω_{6}}$ E^(w2 + w6) + E^(w5) + E^(2w3) + E^(w1 + w6)	5	10	57	256	3
4-241-54-a	$(E^{ω_{3} + ω_{6}})^{\oplus 2} \oplus E^{ω_{5}} \oplus E^{ω_{1} + ω_{2}}$ 2 copies of E^(w3 + w6) + E^(w5) + E^(w1 + w2)	4	8	54	241	2
4-246-55-b	$E^{ω_{3} + ω_{6}} \oplus E^{ω_{5}} \oplus E^{ω_{2} + ω_{3}} \oplus E^{ω_{1} + ω_{6}}$ E^(w3 + w6) + E^(w5) + E^(w2 + w3) + E^(w1 + w6)	4	8	55	246	2