P2 x P2 x P5 – Fano fourfolds

Ambient: ℙ²P2 × ℙ²P2 × ℙ⁵P5 `202050`

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

family	bundle	$\mathrm{h}^{1,1}$	$\mathrm{h}^{2,2}$	$\mathrm{h}^0(X, \omega_X^\vee)$	$\operatorname{vol}(X) = \mathrm{c}_1^4$	$\chi(X, \mathrm{T}_X)$
3-272-60-c	$E^{ω_{3} + ω_{5}} \oplus E^{ω_{4} + ω_{5}} \oplus E^{ω_{2} + ω_{5}}$ E^(w3 + w5) + E^(w4 + w5) + E^(w2 + w5)	3	5	60	272	3
3-288-63-e	$E^{ω_{3} + ω_{5}} \oplus (E^{ω_{2} + ω_{5}})^{\oplus 2}$ E^(w3 + w5) + 2 copies of E^(w2 + w5)	3	7	63	288	2
3-144-36-b	$(E^{ω_{4} + ω_{5}})^{\oplus 2} \oplus E^{2 ω_{1} + ω_{5}}$ 2 copies of E^(w4 + w5) + E^(2w1 + w5)	3	16	36	144	-16
3-146-36-d	$E^{2 ω_{5}} \oplus E^{ω_{3} + ω_{5}} \oplus E^{ω_{1} + ω_{3}} \oplus E^{ω_{2} + ω_{5}}$ E^(2w5) + E^(w3 + w5) + E^(w1 + w3) + E^(w2 + w5)	3	12	36	146	-10
3-146-36-e	$(E^{ω_{3} + ω_{5}})^{\oplus 2} \oplus E^{ω_{1} + ω_{5}} \oplus E^{ω_{2} + ω_{5}}$ 2 copies of E^(w3 + w5) + E^(w1 + w5) + E^(w2 + w5)	3	14	36	146	-12