P2 x Fl(2,3,7) – Fano fourfolds

Ambient: ℙ²P2 × Fl(2, 3, 7) `20605`

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

family	bundle	$\mathrm{h}^{1,1}$	$\mathrm{h}^{2,2}$	$\mathrm{h}^0(X, \omega_X^\vee)$	$\operatorname{vol}(X) = \mathrm{c}_1^4$	$\chi(X, \mathrm{T}_X)$
2-512-105-a	$(E^{ω_{8}})^{\oplus 2} \oplus E^{ω_{2} + ω_{3}}$ 2 copies of E^(w8) + E^(w2 + w3)	2	2	105	512	18
4-385-81-a	$E^{ω_{6}} \oplus E^{ω_{8}} \oplus E^{ω_{2} + ω_{3}}$ E^(w6) + E^(w8) + E^(w2 + w3)	4	7	81	385	12
3-273-60-a	$(E^{ω_{8}})^{\oplus 2} \oplus E^{ω_{3} + ω_{5}} \oplus E^{ω_{1} + ω_{3}}$ 2 copies of E^(w8) + E^(w3 + w5) + E^(w1 + w3)	3	7	60	273	2
3-273-60-b	$(E^{ω_{8}})^{\oplus 2} \oplus E^{ω_{2} + ω_{4}} \oplus E^{ω_{2} + ω_{5}}$ 2 copies of E^(w8) + E^(w2 + w4) + E^(w2 + w5)	3	7	60	273	2
3-272-60-e	$E^{ω_{4}} \oplus (E^{ω_{8}})^{\oplus 2} \oplus E^{2 ω_{5}} \oplus E^{ω_{1} + ω_{3}}$ E^(w4) + 2 copies of E^(w8) + E^(2w5) + E^(w1 + w3)	3	6	60	272	2
3-256-57-k	$E^{ω_{4}} \oplus (E^{ω_{8}})^{\oplus 2} \oplus E^{ω_{1} + ω_{4}} \oplus E^{ω_{2} + ω_{5}}$ E^(w4) + 2 copies of E^(w8) + E^(w1 + w4) + E^(w2 + w5)	3	9	57	256	-2