P1 x P1 x P2 x P4 – Fano fourfolds

Ambient: ℙ¹P1 × ℙ¹P1 × ℙ²P2 × ℙ⁴P4 `112040`

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

family	bundle	$\mathrm{h}^{1,1}$	$\mathrm{h}^{2,2}$	$\mathrm{h}^0(X, \omega_X^\vee)$	$\operatorname{vol}(X) = \mathrm{c}_1^4$	$\chi(X, \mathrm{T}_X)$
4-172-41-a	$E^{ω_{3} + ω_{5}} \oplus E^{ω_{4} + ω_{5}} \oplus E^{ω_{1} + ω_{2} + ω_{5}}$ E^(w3 + w5) + E^(w4 + w5) + E^(w1 + w2 + w5)	4	12	41	172	-6
4-293-64-a	$E^{ω_{4} + ω_{5}} \oplus E^{ω_{2} + ω_{5}} \oplus E^{ω_{1} + ω_{5}}$ E^(w4 + w5) + E^(w2 + w5) + E^(w1 + w5)	4	6	64	293	6
4-352-75-a	$E^{ω_{4} + ω_{5}} \oplus E^{ω_{2} + ω_{5}} \oplus E^{ω_{1} + ω_{3}}$ E^(w4 + w5) + E^(w2 + w5) + E^(w1 + w3)	4	6	75	352	10
4-167-40-a	$E^{ω_{4} + ω_{5}} \oplus E^{ω_{2} + ω_{5}} \oplus E^{ω_{1} + ω_{3} + ω_{5}}$ E^(w4 + w5) + E^(w2 + w5) + E^(w1 + w3 + w5)	4	14	40	167	-8
4-155-38-a	$E^{ω_{4} + ω_{5}} \oplus E^{ω_{2} + 2 ω_{5}} \oplus E^{ω_{1} + ω_{3}}$ E^(w4 + w5) + E^(w2 + 2w5) + E^(w1 + w3)	4	14	38	155	-10
5-184-43-a	$E^{2 ω_{5}} \oplus E^{ω_{4} + ω_{5}} \oplus E^{ω_{1} + ω_{2} + ω_{3}}$ E^(2w5) + E^(w4 + w5) + E^(w1 + w2 + w3)	5	12	43	184	-1
4-167-40-b	$(E^{ω_{3} + ω_{5}})^{\oplus 2} \oplus E^{ω_{2} + ω_{5}} \oplus E^{ω_{1} + ω_{5}}$ 2 copies of E^(w3 + w5) + E^(w2 + w5) + E^(w1 + w5)	4	12	40	167	-6