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On complex \(n\)-folds polarized by an ample line bundle \(L\) with \(\dim\text{Bs}|L|\leq 0, g(L)=q(X)+m\), and \(h^0(L)\geq n+m\). (English) Zbl 1023.14002

Let \(X\) be a complex smooth projective variety of dimension \(n\geq 3\). Let \(K\) be the canonical line bundle and \(L\) an ample line bundle on \(X\). The sectional genus is defined by \(g(L)= 1+ (1/2)(K+(n-1)L) L^{n-1}\). The author had shown that if Bs\(|L |\) is at most finite, then \(g(L)= q(X) +m\) where \(q(X) = h^1({\mathcal O}_X)\) and \(m\) is a positive integer [Y. Fukuma, Can. Math. Bull. 41, 267-278 (1998; Zbl 0955.14040)].
In this paper, the author gives a complete classification of the pairs \((X, L)\) as above with dim Bs\(\mid L \mid \leq 0\) and \(h^0(L) \geq n+m\).

MSC:

14C20 Divisors, linear systems, invertible sheaves
14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)

Citations:

Zbl 0955.14040
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References:

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