Characterizing quasi-affine spherical varieties via the automorphism group
Let $G$ be a connected reductive algebraic group. In this note we prove that for a quasi-affine $G$-spherical variety the weight monoid is determined by the weights of its non-trivial $\mathbb{G}_a$-actions that are homogeneous with respect to a Borel subgroup of $G$. As an application we get that a...
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| creator | Regeta, Andriy van Santen, Immanuel |
| description | Let $G$ be a connected reductive algebraic group. In this note we prove that
for a quasi-affine $G$-spherical variety the weight monoid is determined by the
weights of its non-trivial $\mathbb{G}_a$-actions that are homogeneous with
respect to a Borel subgroup of $G$. As an application we get that a smooth
affine $G$-spherical variety that is non-isomorphic to a torus is determined by
its automorphism group inside the category of smooth affine irreducible
varieties. |
| doi_str_mv | 10.48550/arxiv.1911.10896 |
| format | Article |
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for a quasi-affine $G$-spherical variety the weight monoid is determined by the
weights of its non-trivial $\mathbb{G}_a$-actions that are homogeneous with
respect to a Borel subgroup of $G$. As an application we get that a smooth
affine $G$-spherical variety that is non-isomorphic to a torus is determined by
its automorphism group inside the category of smooth affine irreducible
varieties.</description><identifier>DOI: 10.48550/arxiv.1911.10896</identifier><language>eng</language><subject>Mathematics - Algebraic Geometry</subject><creationdate>2019-11</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,777,882</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1911.10896$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1911.10896$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Regeta, Andriy</creatorcontrib><creatorcontrib>van Santen, Immanuel</creatorcontrib><title>Characterizing quasi-affine spherical varieties via the automorphism group</title><description>Let $G$ be a connected reductive algebraic group. In this note we prove that
for a quasi-affine $G$-spherical variety the weight monoid is determined by the
weights of its non-trivial $\mathbb{G}_a$-actions that are homogeneous with
respect to a Borel subgroup of $G$. As an application we get that a smooth
affine $G$-spherical variety that is non-isomorphic to a torus is determined by
its automorphism group inside the category of smooth affine irreducible
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for a quasi-affine $G$-spherical variety the weight monoid is determined by the
weights of its non-trivial $\mathbb{G}_a$-actions that are homogeneous with
respect to a Borel subgroup of $G$. As an application we get that a smooth
affine $G$-spherical variety that is non-isomorphic to a torus is determined by
its automorphism group inside the category of smooth affine irreducible
varieties.</abstract><doi>10.48550/arxiv.1911.10896</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Algebraic Geometry |
| title | Characterizing quasi-affine spherical varieties via the automorphism group |
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