Module schemes in invariant theory
Let G be a finite group acting linearly on the polynomial ring with invariant ring R. If the action is small, then a classical result of Auslander gives in dimension two a correspondence between linear representations of G and maximal Cohen-Macaulay R-modules. We establish a correspondence for all l...
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| creator | Brenner, Holger |
| description | Let G be a finite group acting linearly on the polynomial ring with invariant
ring R. If the action is small, then a classical result of Auslander gives in
dimension two a correspondence between linear representations of G and maximal
Cohen-Macaulay R-modules. We establish a correspondence for all linear actions
between representations and objects over the invariant ring by looking at
quotient module schemes (up to modification) instead of the modules of
covariants. |
| doi_str_mv | 10.48550/arxiv.2404.10592 |
| format | Article |
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ring R. If the action is small, then a classical result of Auslander gives in
dimension two a correspondence between linear representations of G and maximal
Cohen-Macaulay R-modules. We establish a correspondence for all linear actions
between representations and objects over the invariant ring by looking at
quotient module schemes (up to modification) instead of the modules of
covariants.</description><identifier>DOI: 10.48550/arxiv.2404.10592</identifier><language>eng</language><subject>Mathematics - Algebraic Geometry ; Mathematics - Commutative Algebra ; Mathematics - Representation Theory</subject><creationdate>2024-04</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>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,778,883</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2404.10592$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2404.10592$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Brenner, Holger</creatorcontrib><title>Module schemes in invariant theory</title><description>Let G be a finite group acting linearly on the polynomial ring with invariant
ring R. If the action is small, then a classical result of Auslander gives in
dimension two a correspondence between linear representations of G and maximal
Cohen-Macaulay R-modules. We establish a correspondence for all linear actions
between representations and objects over the invariant ring by looking at
quotient module schemes (up to modification) instead of the modules of
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ring R. If the action is small, then a classical result of Auslander gives in
dimension two a correspondence between linear representations of G and maximal
Cohen-Macaulay R-modules. We establish a correspondence for all linear actions
between representations and objects over the invariant ring by looking at
quotient module schemes (up to modification) instead of the modules of
covariants.</abstract><doi>10.48550/arxiv.2404.10592</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Algebraic Geometry Mathematics - Commutative Algebra Mathematics - Representation Theory |
| title | Module schemes in invariant theory |
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