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Base loci of linear series are numerically determined. (English) Zbl 1017.14017
Take a smooth projective variety $$X$$ and $$L\in\text{Pic}(X)$$. Here the author introduces the stable base locus BS$$(L):= \{x\in X:s(x)=0$$ for every $$s\in H^0(X,L^{\otimes t})$$ and every $$t>0\}$$ and the moving Seshadri constant $$\varepsilon_m (x,L)$$, $$x\in X$$, which measures the local positivity of $$L$$ at $$x$$ if $$L$$ is big. The aim is to obtain in this way generalizations of results known for big and nef line bundles to big line bundles. The aim is very well achieved in this paper: The author shows how the generalized Seshadri constants determine the stable base locus of a big line bundle.

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