Geodesic
PARTIALLY AMPLE LINE BUNDLES ON TORIC VARIETIES
Glasgow mathematical journal, Tome 58 (2016) no. 3, pp. 587-598

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DOI

In this note we study properties of partially ample line bundles on simplicial projective toric varieties. We prove that the cone of q-ample line bundles is a union of rational polyhedral cones, and calculate these cones in examples. We prove a restriction theorem for big q-ample line bundles, and deduce that q-ampleness of the anticanonical bundle is not invariant under flips. Finally we prove a Kodaira-type vanishing theorem for q-ample line bundles. 
BROOMHEAD, NATHAN; OTTEM, JOHN CHRISTIAN; PRENDERGAST-SMITH, ARTIE. PARTIALLY AMPLE LINE BUNDLES ON TORIC VARIETIES. Glasgow mathematical journal, Tome 58 (2016) no. 3, pp. 587-598. doi: 10.1017/S001708951500035X
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     title = {PARTIALLY {AMPLE} {LINE} {BUNDLES} {ON} {TORIC} {VARIETIES}},
     journal = {Glasgow mathematical journal},
     pages = {587--598},
     year = {2016},
     volume = {58},
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     doi = {10.1017/S001708951500035X},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708951500035X/}
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