On the Geometry of Spherical Varieties

Perrin, Nicolás

doi:10.1007/s00031-014-9254-0

Cited by 76 publications

(73 citation statements)

References 136 publications

(140 reference statements)

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“…By the work of M. Brion [Bri93] we have that Q-factorial spherical varieties are Mori dream spaces. An alternative proof of this result can be found in [Per14,Section 4].…”

Section: Mori Chamber and Stable Base Locus Decompositionsmentioning

confidence: 89%

On Mori chamber and stable base locus decompositions

Laface¹,

Massarenti

Rischter

2019

Trans. Amer. Math. Soc.

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The effective cone of a Mori dream space admits two wall-and-chamber decompositions called Mori chamber and stable base locus decompositions. In general the former is a non trivial refinement of the latter. We investigate, from both the geometrical and the combinatorial viewpoints, the differences between these decompositions. Furthermore, we provide a criterion to establish whether the two decompositions coincide for a Mori dream space of Picard rank two, and we construct an explicit example of a Mori dream space of Picard rank two for which the decompositions are different, showing that our criterion is sharp. Finally, we classify the smooth toric 3-folds of Picard rank three for which the two decompositions are different.

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“…By the work of M. Brion [Bri93] we have that Q-factorial spherical varieties are Mori dream spaces. An alternative proof of this result can be found in [Per14,Section 4].…”

Section: Mori Chamber and Stable Base Locus Decompositionsmentioning

confidence: 89%

On Mori chamber and stable base locus decompositions

Laface¹,

Massarenti

Rischter

2019

Trans. Amer. Math. Soc.

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“…(2) X comes equipped with the action of a connected, reductive algebraic group G; (3) X has finitely many B-orbits, where B ⊂ G is a Borel subgroup. These are well studied so that we may hope to transport their properties to rep Q (d) (see the survey [Per14]).…”

Section: Open Problemsmentioning

confidence: 99%

K-polynomials of type A quiver orbit closures and lacing diagrams

Kinser¹

2018

Representations of Algebras

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“…Many authors have studied variants of the problem. For instance, Magyar, Weyman and Zelevinsky have classified instances when the action of G on the product has finitely many orbits [8] (see also [6,7,9,10,13] for related literature).…”

Section: Introductionmentioning

confidence: 99%