P2 x Gr(2,5) – Fano fourfolds

Ambient: ℙ²P2 × Gr(2, 5) `2041`

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

family	bundle	$\mathrm{h}^{1,1}$	$\mathrm{h}^{1,2}$	$\mathrm{h}^{1,3}$	$\mathrm{h}^{2,2}$	$\mathrm{h}^0(X, \omega_X^\vee)$	$\operatorname{vol}(X) = \mathrm{c}_1^4$	$\chi(X, \mathrm{T}_X)$
2-513-105-b	$E^{ω_{2} + ω_{3}}$ E^(w2 + w3)	2	0	0	3	105	513	18
2-75-22-a	$(E^{ω_{4}})^{\oplus 2} \oplus (E^{ω_{1} + ω_{4}})^{\oplus 2}$ 2 copies of E^(w4) + 2 copies of E^(w1 + w4)	2	0	2	32	22	75	-28
2-90-25-b	$E^{ω_{3} + ω_{4}} \oplus E^{ω_{1} + ω_{3}}$ E^(w3 + w4) + E^(w1 + w3)	2	0	0	19	25	90	-21
2-288-63-a	$(E^{ω_{4}})^{\oplus 2} \oplus E^{ω_{1} + ω_{3}}$ 2 copies of E^(w4) + E^(w1 + w3)	2	0	0	4	63	288	2
2-74-22-b	$E^{ω_{4}} \oplus E^{2 ω_{4}} \oplus E^{ω_{1} + ω_{3}}$ E^(w4) + E^(2w4) + E^(w1 + w3)	2	0	1	30	22	74	-30
2-165-40-a	$(E^{ω_{4}})^{\oplus 2} \oplus E^{ω_{2} + ω_{4}}$ 2 copies of E^(w4) + E^(w2 + w4)	2	1	0	4	40	165	-7
2-160-39-f	$(E^{ω_{4}})^{\oplus 3} \oplus E^{ω_{1} + ω_{4}}$ 3 copies of E^(w4) + E^(w1 + w4)	2	0	0	7	39	160	-9
2-85-24-b	$(E^{ω_{2} + ω_{4}})^{\oplus 2}$ 2 copies of E^(w2 + w4)	2	0	0	22	24	85	-24
2-80-23-d	$E^{ω_{4}} \oplus E^{ω_{1} + ω_{4}} \oplus E^{ω_{2} + ω_{4}}$ E^(w4) + E^(w1 + w4) + E^(w2 + w4)	2	0	1	27	23	80	-26
2-70-21-d	$(E^{ω_{4}})^{\oplus 3} \oplus E^{2 ω_{1} + ω_{4}}$ 3 copies of E^(w4) + E^(2w1 + w4)	2	0	3	37	21	70	-30