WHAT IS...Essential Dimension?

Reichstein, Zinovy

doi:10.1090/noti909

Cited by 8 publications

(7 citation statements)

References 2 publications

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“…, a n ) but not over any proper subfield. This proves that in fact ed k Rep Q,n = n. See [22] for the details.…”

Section: Essential Dimension Of Functorsmentioning

confidence: 58%

Essential dimension and genericity for quiver representations

Scavia¹

2018

Preprint

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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.

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“…, a n ) but not over any proper subfield. This proves that in fact ed k Rep Q,n = n. See [22] for the details.…”

Section: Essential Dimension Of Functorsmentioning

confidence: 58%

Essential dimension and genericity for quiver representations

Scavia¹

2018

Preprint

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“…Case I. We need to consider the groups ST 28 -ST 32 , ST 34 , ST 35 and ST 37 , with p = 2. With the exception of ST 32 , each of these groups has a reflection of order 2 and thus is ruled out by Proposition 3.1(e).…”

Section: Conclusion Of the Proof Of Theorem 11(b)mentioning

confidence: 99%

“…Case II. Here p = 3 and we need to consider only two groups: ST 34 and ST 35 . The group ST 35 has trivial centre and thus is ruled out by Proposition 3.1(c).…”

Section: Conclusion Of the Proof Of Theorem 11(b)mentioning

confidence: 99%

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Pseudo-reflection groups and essential dimension

Duncan

Reichstein

2014

Journal of the London Mathematical Society

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“…For example, it is used to bound the minimum number of parameters of generic Galois extensions (see [5,Section 8.2]). The introductory article [14] and the survey papers [12] and [13] explain the theory of essential dimension and its applications.…”

Section: Introductionmentioning

confidence: 99%

Simplifying matrix differential equations with general coefficients

Cheung¹

2022

Preprint

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We show that the n × n matrix differential equation δ(Y ) = AY with n 2 general coefficients cannot be simplified to an equation in less than n parameters by using gauge transformations whose coefficients are rational functions in the matrix entries of A and their derivatives. Our proof uses differential Galois theory and a differential analogue of essential dimension. We also bound the minimum number of parameters needed to describe some generic Picard-Vessiot extensions.

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WHAT IS...Essential Dimension?

Cited by 8 publications

References 2 publications

Essential dimension and genericity for quiver representations

Essential dimension and genericity for quiver representations

Pseudo-reflection groups and essential dimension

Simplifying matrix differential equations with general coefficients

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