P3 x Fl(1,4,6) – Fano fourfolds

Ambient: ℙ³P3 × Fl(1, 4, 6) `3058`

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

family	bundle	$\mathrm{h}^{1,1}$	$\mathrm{h}^{2,2}$	$\mathrm{h}^0(X, \omega_X^\vee)$	$\operatorname{vol}(X) = \mathrm{c}_1^4$	$\chi(X, \mathrm{T}_X)$
3-378-80-a	$(E^{ω_{4}})^{\oplus 3} \oplus E^{ω_{7}} \oplus E^{ω_{3} + ω_{8}}$ 3 copies of E^(w4) + E^(w7) + E^(w3 + w8)	3	4	80	378	10
3-282-62-b	$E^{ω_{5}} \oplus E^{ω_{1} + ω_{4}} \oplus E^{ω_{3} + ω_{8}}$ E^(w5) + E^(w1 + w4) + E^(w3 + w8)	3	6	62	282	2
3-282-62-c	$E^{ω_{7}} \oplus E^{ω_{3} + ω_{4}} \oplus E^{ω_{3} + ω_{8}}$ E^(w7) + E^(w3 + w4) + E^(w3 + w8)	3	6	62	282	2
2-176-42-c	$E^{ω_{8}} \oplus E^{2 ω_{4}} \oplus E^{ω_{1} + ω_{4}} \oplus E^{ω_{3} + ω_{8}}$ E^(w8) + E^(2w4) + E^(w1 + w4) + E^(w3 + w8)	2	10	42	176	-11
3-225-51-b	$(E^{ω_{4}})^{\oplus 3} \oplus E^{ω_{1} + ω_{7}} \oplus E^{ω_{3} + ω_{8}}$ 3 copies of E^(w4) + E^(w1 + w7) + E^(w3 + w8)	3	11	51	225	-5
3-240-54-c	$(E^{ω_{4}})^{\oplus 2} \oplus E^{ω_{7}} \oplus E^{ω_{1} + ω_{4}} \oplus E^{ω_{3} + ω_{8}}$ 2 copies of E^(w4) + E^(w7) + E^(w1 + w4) + E^(w3 + w8)	3	8	54	240	-2
3-230-52-a	$E^{ω_{7}} \oplus (E^{ω_{8}})^{\oplus 2} \oplus E^{ω_{1} + ω_{8}} \oplus E^{ω_{3} + ω_{4}}$ E^(w7) + 2 copies of E^(w8) + E^(w1 + w8) + E^(w3 + w4)	3	6	52	230	0