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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
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