Fano fourfolds of type A beta

zero loci on products of type A Grassmannians and flag varieties

Ambient: Fl(1, 3, 5) `44`

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

family	bundle	$\mathrm{h}^{1,1}$	$\mathrm{h}^{1,2}$	$\mathrm{h}^{1,3}$	$\mathrm{h}^{2,2}$	$\mathrm{h}^0(X, \omega_X^\vee)$	$\operatorname{vol}(X) = \mathrm{c}_1^4$	$\chi(X, \mathrm{T}_X)$
3-405-85-a	$(E^{ω_{3}})^{\oplus 2} \oplus E^{ω_{4}}$ 2 copies of E^(w3) + E^(w4)	3	0	0	4	85	405	12
2-384-81-a	$E^{ω_{1}} \oplus E^{2 ω_{4}}$ E^(w1) + E^(2w4)	2	0	0	2	81	384	10
2-433-90-a	$(E^{ω_{2}})^{\oplus 2}$ 2 copies of E^(w2)	2	0	0	3	90	433	13
2-273-60-a	$E^{ω_{4}} \oplus E^{ω_{1} + ω_{4}}$ E^(w4) + E^(w1 + w4)	2	0	0	3	60	273	3
2-240-54-e	$E^{ω_{3}} \oplus E^{ω_{4}} \oplus E^{2 ω_{1}}$ E^(w3) + E^(w4) + E^(2w1)	2	0	0	2	54	240	1
2-192-45-g	$E^{2 ω_{1}} \oplus E^{2 ω_{4}}$ E^(2w1) + E^(2w4)	2	2	0	2	45	192	-4
2-277-61-a	$E^{ω_{2}} \oplus (E^{ω_{3}})^{\oplus 2}$ E^(w2) + 2 copies of E^(w3)	2	0	0	4	61	277	1
2-115-30-a	$E^{ω_{2}} \oplus E^{ω_{3}} \oplus E^{ω_{1} + ω_{3}}$ E^(w2) + E^(w3) + E^(w1 + w3)	2	0	1	24	30	115	-23
2-116-30-a	$(E^{ω_{3}})^{\oplus 2} \oplus E^{ω_{1} + ω_{4}}$ 2 copies of E^(w3) + E^(w1 + w4)	2	0	0	13	30	116	-14
2-224-51-b	$E^{ω_{3}} \oplus E^{ω_{4}} \oplus E^{ω_{1} + ω_{3}}$ E^(w3) + E^(w4) + E^(w1 + w3)	2	0	0	7	51	224	-5
2-69-21-a	$E^{ω_{3}} \oplus E^{ω_{4}} \oplus E^{2 ω_{1} + ω_{3}}$ E^(w3) + E^(w4) + E^(2w1 + w3)	2	0	5	52	21	69	-40
2-96-26-a	$E^{ω_{4}} \oplus E^{2 ω_{1}} \oplus E^{2 ω_{3}}$ E^(w4) + E^(2w1) + E^(2w3)	2	2	0	10	26	96	-13
2-85-24-a	$E^{ω_{4}} \oplus (E^{ω_{1} + ω_{3}})^{\oplus 2}$ E^(w4) + 2 copies of E^(w1 + w3)	2	0	2	32	24	85	-28
2-224-51-c	$E^{ω_{1}} \oplus (E^{ω_{3}})^{\oplus 3}$ E^(w1) + 3 copies of E^(w3)	2	0	0	3	51	224	-1
2-95-26-a	$E^{ω_{1}} \oplus (E^{ω_{3}})^{\oplus 2} \oplus E^{ω_{1} + ω_{3}}$ E^(w1) + 2 copies of E^(w3) + E^(w1 + w3)	2	0	1	23	26	95	-22
2-116-30-b	$(E^{ω_{3}})^{\oplus 3} \oplus E^{2 ω_{1}}$ 3 copies of E^(w3) + E^(2w1)	2	0	0	10	30	116	-11