Geodesic
Essential Dimension and Genericity for Quiver Representations
Documenta mathematica, Tome 25 (2020), pp. 329-364
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We study the essential dimension of representations of a fixed quiver with given dimension vector. We also consider the question of when the genericity property holds, i.e., when essential dimension and generic essential dimension agree. We classify the quivers satisfying the genericity property for every dimension vector and show that for every wild quiver the genericity property holds for infinitely many of its Schur roots. We also construct a large class of examples, where the genericity property fails. Our results are particularly detailed in the case of Kronecker quivers.
DOI : 10.4171/dm/749
Classification : 14A20, 16G20
Mots-clés : essential dimension, quiver representations, genericity property, algebraic stack 
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     author = {Federico Scavia},
     title = {Essential {Dimension} and {Genericity} for {Quiver} {Representations}},
     journal = {Documenta mathematica},
     pages = {329--364},
     year = {2020},
     volume = {25},
     doi = {10.4171/dm/749},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/749/}
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Federico Scavia. Essential Dimension and Genericity for Quiver Representations. Documenta mathematica, Tome 25 (2020), pp. 329-364. doi: 10.4171/dm/749

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