caa a22 4500 445835702 CHVBK 20180317145329.0 cr unu---uuuuu 170323e20110601xx s 000 0 eng 10.1007/s00209-010-0666-9 doi (NATIONALLICENCE)springer-10.1007/s00209-010-0666-9 Jow Shin-Yao Department of Mathematics, University of Pennsylvania, Philadelphia, PA, USA aut A Lefschetz hyperplane theorem for Mori dream spaces [Elektronische Daten] [Shin-Yao Jow] Let X be a smooth Mori dream space of dimension ≥ 4. We show that, if X satisfies a suitable GIT condition which we call small unstable locus, then every smooth ample divisor Y of X is also a Mori dream space. Moreover, the restriction map identifies the Néron-Severi spaces of X and Y, and under this identification every Mori chamber of Y is a union of some Mori chambers of X, and the nef cone of Y is the same as the nef cone of X. This Lefschetz-type theorem enables one to construct many examples of Mori dream spaces by taking "Mori dream hypersurfaces” of an ambient Mori dream space, provided that it satisfies the GIT condition. To facilitate this, we then show that the GIT condition is stable under taking products and taking the projective bundle of the direct sum of at least three line bundles, and in the case when X is toric, we show that the condition is equivalent to the fan of X being 2-neighborly. Springer-Verlag, 2010 Mori dream space nationallicence Lefschetz theorem nationallicence Nef cone nationallicence Mori chamber nationallicence m -neighborly fan nationallicence Cox ring nationallicence GIT quotient nationallicence Mathematische Zeitschrift Springer-Verlag 268/1-2(2011-06-01), 197-209 0025-5874 268:1-2<197 2011 268 209 https://doi.org/10.1007/s00209-010-0666-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-010-0666-9 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Jow Shin-Yao Department of Mathematics, University of Pennsylvania, Philadelphia, PA, USA aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 268/1-2(2011-06-01), 197-209 0025-5874 268:1-2<197 2011 268 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer