The family of lines on the Fano threefold V5
1989 ◽
Vol 116
◽
pp. 111-122
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Keyword(s):
A smooth projective algebraic 3-fold V over the field C is called a Fano 3-fold if the anticanonical divisor — Kv is ample. The integer g = g(V) = ½(- Kv)3 is called the genus of the Fano 3-fold V. The maximal integer r ≧ 1 such that ϑ(— Kv)≃ ℋ r for some (ample) invertible sheaf ℋ ε Pic V is called the index of the Fano 3-fold V. Let V be a Fano 3-fold of the index r = 2 and the genus g = 21 which has the second Betti number b2(V) = 1. Then V can be embedded in P6 with degree 5, by the linear system |ℋ|, where ϑ(— Kv)≃ ℋ2 (see Iskovskih [5]). We denote this Fano 3-fold V by V5.
2007 ◽
Vol 18
(10)
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pp. 1187-1224
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Keyword(s):
2002 ◽
Vol 45
(3)
◽
pp. 349-354
◽
Keyword(s):
2000 ◽
Vol 41
(1)
◽
pp. 133-136
1988 ◽
Vol 62
(03)
◽
pp. 419-423
◽
Keyword(s):
1971 ◽
Vol 29
◽
pp. 258-259
◽
Keyword(s):
1990 ◽
Vol 48
(3)
◽
pp. 600-601