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Stable base locus decompositions of Kontsevich moduli spaces. (English) Zbl 1200.14050
In this paper, the authors study the birational geometry of the Kontsevich space of genus $$0$$ unmarked stable maps to Grassmannians $$\overline M_{0,0}(\mathbb G(k, n), d)$$. The effective cone is decomposed into chambers according to the stable base locus of the linear series, and the $$8$$ chambers for degree $$d=2$$ and the $$22$$ chambers for degree $$d=3$$ are explicitly found. The birational models arising from each chamber in the decomposition are also found, and given modular interpretation in most cases.

##### MSC:
 14H10 Families, moduli of curves (algebraic) 14E05 Rational and birational maps 14D20 Algebraic moduli problems, moduli of vector bundles
##### Keywords:
Kontsevich space; compactifications; birational geometry
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##### References:
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