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Linear bounds for levels of stable rationality

Fedor Bogomolov, Christian Böhning, Hans-Christian Graf von Bothmer (2012)

Open Mathematics

Let G be one of the groups SLn(ℂ), Sp2n (ℂ), SOm(ℂ), Om(ℂ), or G 2. For a generically free G-representation V, we say that N is a level of stable rationality for V/G if V/G × ℙN is rational. In this paper we improve known bounds for the levels of stable rationality for the quotients V/G. In particular, their growth as functions of the rank of the group is linear for G being one of the classical groups.

Problemi di razionalità ed unirazionalità in geometria algebrica

Alessandro Verra (2005)

Bollettino dell'Unione Matematica Italiana

Il presente articolo è una versione allargata della omonima conferenza tenuta a Milano durante il XVII convegno nazionale UMI nel settembre 2003. L'articolo ha come abiettivo principale quello di presentare una introduzione, il più possibile elementare, ai problemi di razionalità/unirazionalità in geometria algebrica. Avendo come punto di riferimento l'esempio delle ipersuperfici dello spazio proiettivo complesso, in particolare le ipersuperfici cubiche, vengono presentati temi classici e problemi...

Rationality of the quotient of ℙ2 by finite group of automorphisms over arbitrary field of characteristic zero

Andrey Trepalin (2014)

Open Mathematics

Let 𝕜 be a field of characteristic zero and G be a finite group of automorphisms of projective plane over 𝕜 . Castelnuovo’s criterion implies that the quotient of projective plane by G is rational if the field 𝕜 is algebraically closed. In this paper we prove that 𝕜 2 𝕜 2 G G is rational for an arbitrary field 𝕜 of characteristic zero.

Stable cohomology of alternating groups

Fedor Bogomolov, Christian Böhning (2014)

Open Mathematics

We determine the stable cohomology groups ( H S i 𝔄 n , 𝔄 n , p p of the alternating groups 𝔄 n for all integers n and i, and all odd primes p.

Unramified Brauer group of the moduli spaces of PGLr(ℂ)-bundles over curves

Indranil Biswas, Amit Hogadi, Yogish Holla (2014)

Open Mathematics

Let X be an irreducible smooth complex projective curve of genus g, with g ≥ 2. Let N be a connected component of the moduli space of semistable principal PGLr (ℂ)-bundles over X; it is a normal unirational complex projective variety. We prove that the Brauer group of a desingularization of N is trivial.

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