Fano fourfolds of type A beta

zero loci on products of type A Grassmannians and flag varieties

Ambient: ℙ²P2 × Fl(1, 3, 5) `2044`

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

family	bundle	$\mathrm{h}^{1,1}$	$\mathrm{h}^{1,2}$	$\mathrm{h}^{1,3}$	$\mathrm{h}^{2,2}$	$\mathrm{h}^0(X, \omega_X^\vee)$	$\operatorname{vol}(X) = \mathrm{c}_1^4$	$\chi(X, \mathrm{T}_X)$
4-293-64-a	$(E^{ω_{5}})^{\oplus 2} \oplus E^{ω_{6}} \oplus E^{ω_{2} + ω_{3}}$ 2 copies of E^(w5) + E^(w6) + E^(w2 + w3)	4	0	0	6	64	293	6
3-352-75-a	$E^{ω_{3}} \oplus E^{ω_{5}} \oplus E^{ω_{2} + ω_{6}}$ E^(w3) + E^(w5) + E^(w2 + w6)	3	0	0	5	75	352	8
3-199-46-a	$E^{ω_{6}} \oplus E^{ω_{2} + ω_{3}} \oplus E^{ω_{2} + ω_{5}}$ E^(w6) + E^(w2 + w3) + E^(w2 + w5)	3	0	0	8	46	199	-3
3-417-87-a	$E^{ω_{4}} \oplus E^{ω_{2} + ω_{6}}$ E^(w4) + E^(w2 + w6)	3	0	0	5	87	417	13
3-211-48-b	$E^{ω_{6}} \oplus E^{ω_{2} + ω_{4}}$ E^(w6) + E^(w2 + w4)	3	0	0	7	48	211	0
3-225-51-a	$E^{ω_{3} + ω_{6}} \oplus E^{ω_{2} + ω_{6}}$ E^(w3 + w6) + E^(w2 + w6)	3	0	0	10	51	225	-4
3-193-45-c	$E^{ω_{3}} \oplus E^{ω_{3} + ω_{5}} \oplus E^{ω_{2} + ω_{6}}$ E^(w3) + E^(w3 + w5) + E^(w2 + w6)	3	0	0	12	45	193	-8
3-273-60-c	$(E^{ω_{4}})^{\oplus 2} \oplus E^{ω_{1} + ω_{6}}$ 2 copies of E^(w4) + E^(w1 + w6)	3	0	0	5	60	273	4
3-208-48-f	$E^{ω_{5}} \oplus E^{2 ω_{3}} \oplus E^{ω_{2} + ω_{6}}$ E^(w5) + E^(2w3) + E^(w2 + w6)	3	0	0	6	48	208	-2
3-310-67-a	$(E^{ω_{6}})^{\oplus 2} \oplus E^{ω_{1} + ω_{4}}$ 2 copies of E^(w6) + E^(w1 + w4)	3	0	0	5	67	310	6
3-183-43-b	$E^{ω_{5}} \oplus E^{ω_{6}} \oplus E^{ω_{1} + ω_{5}} \oplus E^{ω_{2} + ω_{3}}$ E^(w5) + E^(w6) + E^(w1 + w5) + E^(w2 + w3)	3	0	0	9	43	183	-5
4-167-40-c	$(E^{ω_{5}})^{\oplus 2} \oplus E^{ω_{6}} \oplus (E^{ω_{1} + ω_{3}})^{\oplus 2}$ 2 copies of E^(w5) + E^(w6) + 2 copies of E^(w1 + w3)	4	0	0	12	40	167	-6