P1 x P2 x P5 – Fano fourfolds

Ambient: ℙ¹P1 × ℙ²P2 × ℙ⁵P5 `12050`

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

family	bundle	$\mathrm{h}^{1,1}$	$\mathrm{h}^{1,2}$	$\mathrm{h}^{1,3}$	$\mathrm{h}^{2,2}$	$\mathrm{h}^0(X, \omega_X^\vee)$	$\operatorname{vol}(X) = \mathrm{c}_1^4$	$\chi(X, \mathrm{T}_X)$
3-218-50-b	$E^{2 ω_{4}} \oplus E^{ω_{3} + ω_{4}} \oplus E^{ω_{1} + ω_{4}}$ E^(2w4) + E^(w3 + w4) + E^(w1 + w4)	3	0	0	6	50	218	-2
3-110-29-c	$E^{2 ω_{4}} \oplus E^{ω_{3} + ω_{4}} \oplus E^{ω_{1} + ω_{2} + ω_{4}}$ E^(2w4) + E^(w3 + w4) + E^(w1 + w2 + w4)	3	0	1	24	29	110	-20
3-81-24-a	$E^{3 ω_{4}} \oplus E^{ω_{3} + ω_{4}} \oplus E^{ω_{1} + ω_{2}}$ E^(3w4) + E^(w3 + w4) + E^(w1 + w2)	3	1	1	30	24	81	-31
3-104-28-c	$E^{ω_{2} + ω_{4}} \oplus E^{ω_{3} + ω_{4}} \oplus E^{ω_{1} + 2 ω_{4}}$ E^(w2 + w4) + E^(w3 + w4) + E^(w1 + 2w4)	3	0	1	27	28	104	-24
3-99-27-a	$E^{ω_{2} + 2 ω_{4}} \oplus E^{ω_{3} + ω_{4}} \oplus E^{ω_{1} + ω_{4}}$ E^(w2 + 2w4) + E^(w3 + w4) + E^(w1 + w4)	3	0	1	30	27	99	-27
3-104-28-d	$(E^{2 ω_{4}})^{\oplus 2} \oplus E^{ω_{2} + ω_{4}} \oplus E^{ω_{1} + ω_{2}}$ 2 copies of E^(2w4) + E^(w2 + w4) + E^(w1 + w2)	3	2	0	12	28	104	-14
3-110-29-d	$E^{2 ω_{4}} \oplus (E^{ω_{2} + ω_{4}})^{\oplus 2} \oplus E^{ω_{1} + ω_{4}}$ E^(2w4) + 2 copies of E^(w2 + w4) + E^(w1 + w4)	3	0	0	18	29	110	-17