P3 x Gr(2,4) – Fano fourfolds

Ambient: ℙ³P3 × Gr(2, 4) `3031`

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

family	bundle	$\mathrm{h}^{1,1}$	$\mathrm{h}^{1,2}$	$\mathrm{h}^{1,3}$	$\mathrm{h}^{2,2}$	$\mathrm{h}^0(X, \omega_X^\vee)$	$\operatorname{vol}(X) = \mathrm{c}_1^4$	$\chi(X, \mathrm{T}_X)$
2-90-24-a	$E^{ω_{1} + 2 ω_{4}}$ E^(w1 + 2w4)	2	0	0	12	24	90	-9
2-192-45-a	$E^{ω_{2} + ω_{5}}$ E^(w2 + w5)	2	2	0	2	45	192	-4
3-350-75-a	$E^{ω_{3} + ω_{5}}$ E^(w3 + w5)	3	0	0	4	75	350	7
2-176-42-b	$E^{ω_{5}} \oplus (E^{ω_{1} + ω_{5}})^{\oplus 2}$ E^(w5) + 2 copies of E^(w1 + w5)	2	0	0	10	42	176	-11
2-60-19-a	$E^{ω_{5}} \oplus E^{ω_{1} + ω_{5}} \oplus E^{2 ω_{1} + ω_{5}}$ E^(w5) + E^(w1 + w5) + E^(2w1 + w5)	2	0	5	52	19	60	-39
2-70-21-a	$(E^{ω_{1} + ω_{5}})^{\oplus 3}$ 3 copies of E^(w1 + w5)	2	0	3	40	21	70	-33