P1 x P2 x Gr(2,5) – Fano fourfolds

Ambient: ℙ¹P1 × ℙ²P2 × Gr(2, 5) `12041`

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

family	bundle	$\mathrm{h}^{1,1}$	$\mathrm{h}^{1,2}$	$\mathrm{h}^{1,3}$	$\mathrm{h}^{2,2}$	$\mathrm{h}^0(X, \omega_X^\vee)$	$\operatorname{vol}(X) = \mathrm{c}_1^4$	$\chi(X, \mathrm{T}_X)$
3-352-75-c	$E^{ω_{3} + ω_{4}} \oplus E^{ω_{1} + ω_{5}}$ E^(w3 + w4) + E^(w1 + w5)	3	0	0	5	75	352	8
3-113-30-b	$E^{ω_{3} + ω_{4}} \oplus E^{ω_{1} + 2 ω_{5}}$ E^(w3 + w4) + E^(w1 + 2w5)	3	0	2	33	30	113	-28
3-141-35-c	$(E^{ω_{5}})^{\oplus 2} \oplus E^{ω_{2} + ω_{4}} \oplus E^{ω_{1} + ω_{5}}$ 2 copies of E^(w5) + E^(w2 + w4) + E^(w1 + w5)	3	0	0	12	35	141	-10
3-135-34-a	$(E^{ω_{5}})^{\oplus 2} \oplus E^{ω_{3} + ω_{5}} \oplus E^{ω_{1} + ω_{2}}$ 2 copies of E^(w5) + E^(w3 + w5) + E^(w1 + w2)	3	1	0	9	34	135	-9
3-130-33-d	$(E^{ω_{5}})^{\oplus 3} \oplus E^{ω_{2} + ω_{5}} \oplus E^{ω_{1} + ω_{2}}$ 3 copies of E^(w5) + E^(w2 + w5) + E^(w1 + w2)	3	0	0	12	33	130	-11