P2 x P4 x P5 – Fano fourfolds

Ambient: ℙ²P2 × ℙ⁴P4 × ℙ⁵P5 `204050`

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

family	bundle	$\mathrm{h}^{1,1}$	$\mathrm{h}^{1,3}$	$\mathrm{h}^{2,2}$	$\mathrm{h}^0(X, \omega_X^\vee)$	$\operatorname{vol}(X) = \mathrm{c}_1^4$	$\chi(X, \mathrm{T}_X)$
3-416-87-a	$E^{ω_{6} + ω_{7}} \oplus E^{ω_{1} + ω_{3}} \oplus E^{ω_{2} + ω_{3}}$ E^(w6 + w7) + E^(w1 + w3) + E^(w2 + w3)	3	0	4	87	416	13
3-176-42-c	$E^{ω_{6} + ω_{7}} \oplus E^{ω_{1} + ω_{3} + ω_{7}} \oplus E^{ω_{2} + ω_{3}}$ E^(w6 + w7) + E^(w1 + w3 + w7) + E^(w2 + w3)	3	1	23	42	176	-18
3-193-45-a	$E^{ω_{3} + ω_{7}} \oplus E^{ω_{6} + ω_{7}} \oplus (E^{ω_{1} + ω_{3}})^{\oplus 2}$ E^(w3 + w7) + E^(w6 + w7) + 2 copies of E^(w1 + w3)	3	0	11	45	193	-7
3-198-46-b	$E^{ω_{6} + ω_{7}} \oplus E^{2 ω_{3}} \oplus E^{ω_{1} + ω_{7}} \oplus E^{ω_{1} + ω_{3}}$ E^(w6 + w7) + E^(2w3) + E^(w1 + w7) + E^(w1 + w3)	3	0	10	46	198	-6