Fano fourfolds of type A beta

zero loci on products of type A Grassmannians and flag varieties

Ambient: ℙ¹P1 × ℙ²P2 × ℙ²P2 × ℙ³P3 `1202030`

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

family	bundle	$\mathrm{h}^{1,1}$	$\mathrm{h}^{1,2}$	$\mathrm{h}^{1,3}$	$\mathrm{h}^{2,2}$	$\mathrm{h}^0(X, \omega_X^\vee)$	$\operatorname{vol}(X) = \mathrm{c}_1^4$	$\chi(X, \mathrm{T}_X)$
4-314-68-a	$E^{ω_{4} + ω_{6}} \oplus E^{ω_{3} + ω_{6}} \oplus E^{ω_{1} + ω_{4}}$ E^(w4 + w6) + E^(w3 + w6) + E^(w1 + w4)	4	0	0	6	68	314	7
4-320-69-a	$E^{ω_{4} + ω_{6}} \oplus E^{ω_{3} + ω_{6}} \oplus E^{ω_{1} + ω_{2}}$ E^(w4 + w6) + E^(w3 + w6) + E^(w1 + w2)	4	0	0	7	69	320	7
4-188-44-b	$E^{ω_{4} + ω_{6}} \oplus E^{ω_{3} + ω_{6}} \oplus E^{ω_{1} + ω_{2} + ω_{4}}$ E^(w4 + w6) + E^(w3 + w6) + E^(w1 + w2 + w4)	4	0	0	12	44	188	-5
4-320-69-b	$E^{ω_{5} + ω_{6}} \oplus E^{ω_{2} + ω_{4}} \oplus E^{ω_{1} + ω_{6}}$ E^(w5 + w6) + E^(w2 + w4) + E^(w1 + w6)	4	0	0	6	69	320	8
4-352-75-b	$E^{ω_{5} + ω_{6}} \oplus E^{ω_{2} + ω_{4}} \oplus E^{ω_{1} + ω_{2}}$ E^(w5 + w6) + E^(w2 + w4) + E^(w1 + w2)	4	0	0	6	75	352	10
4-182-43-c	$E^{ω_{5} + ω_{6}} \oplus E^{ω_{2} + ω_{4}} \oplus E^{ω_{1} + ω_{2} + ω_{6}}$ E^(w5 + w6) + E^(w2 + w4) + E^(w1 + w2 + w6)	4	0	0	12	43	182	-6
4-182-43-d	$E^{ω_{5} + ω_{6}} \oplus E^{ω_{2} + ω_{4} + ω_{6}} \oplus E^{ω_{1} + ω_{2}}$ E^(w5 + w6) + E^(w2 + w4 + w6) + E^(w1 + w2)	4	0	0	14	43	182	-8
4-176-42-a	$E^{ω_{5} + ω_{6}} \oplus E^{2 ω_{2} + ω_{6}} \oplus E^{ω_{1} + ω_{4}}$ E^(w5 + w6) + E^(2w2 + w6) + E^(w1 + w4)	4	0	0	10	42	176	-5
4-194-45-a	$E^{ω_{5} + ω_{6}} \oplus E^{2 ω_{2} + ω_{4}} \oplus E^{ω_{1} + ω_{6}}$ E^(w5 + w6) + E^(2w2 + w4) + E^(w1 + w6)	4	0	0	9	45	194	-1
4-188-44-d	$(E^{ω_{4} + ω_{6}})^{\oplus 2} \oplus E^{ω_{2} + ω_{6}} \oplus E^{ω_{1} + ω_{2}}$ 2 copies of E^(w4 + w6) + E^(w2 + w6) + E^(w1 + w2)	4	0	0	9	44	188	-2