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Linear bounds for levels of stable rationality

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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.
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  • [1] Antonyan L.V., Classification of four-vectors of an eight-dimensional space, Trudy Sem. Vektor. Tenzor. Anal., 1981, 20, 144–161 (in Russian)
  • [2] Beauville A., Determinantal hypersurfaces, Michigan Math. J., 2000, 48, 39–64
  • [3] Bogomolov F.A., Stable rationality of quotient varieties by simply connected groups, Mat. Sb. (N.S.), 1986, 130(1), 3–17 (in Russian)
  • [4] Bogomolov F.A., Rationality of the moduli of hyperelliptic curves of arbitrary genus, In: Conference in Algebraic Geometry, Vancouver, 1984, CMS Conf. Proc., 6, American Mathematical Society, Providence, 1986, 17–37
  • [5] Bogomolov F., Böhning Chr., Graf von Bothmer H.-Chr., Rationality of quotients by linear actions of affine groups, Sci. China Math. (in press), DOI: 10.1007/s11425-010-4127-z
  • [6] Bogomolov F.A., Katsylo P.I., Rationality of some quotient varieties, Mat. Sb. (N.S.), 1985, 126(4), 584–589 (in Russian)
  • [7] Dolgachev I.V., Rationality of fields of invariants, In: Algebraic Geometry, Brunswick, 1985, Proc. Sympos. Pure Math., 46(2), American Mathematical Society, Providence, 1987, 3–16
  • [8] Fulton W., Harris J., Representation Theory, Grad. Texts in Math., 129, Springer, New York, 1991
  • [9] Gille P., Szamuely T., Central Simple Algebras and Galois Cohomology, Cambridge Stud. Adv. Math., 101, Cambridge University Press, Cambridge, 2006
  • [10] Goodman R., Wallach N.R., Symmetry, Representations, and Invariants, Grad. Texts in Math., 255, Springer, Dordrecht, 2009
  • [11] Hoffmann N., Moduli stacks of vector bundles on curves and the King-Schofield rationality proof, In: Cohomological and Geometric Approaches to Rationality Problems, Progr. Math., 282, Birkhäuser, Boston, 2010, 133–148
  • [12] Katanova A.A., Explicit form of certain multivector invariants, In: Lie Groups, their Discrete Subgroups, and Invariant Theory, Adv. Soviet Math., 8, American Mathematical Society, Providence, 1992, 87–93
  • [13] Katsylo P.I., Rationality of orbit spaces of irreducible representations of the group SL2, Izv. Akad. Nauk SSSR Ser. Mat., 1983, 47(1), 26–36 (in Russian)
  • [14] Katsylo P.I., Rationality of the moduli spaces of hyperelliptic curves, Izv. Akad. Nauk SSSR Ser. Mat., 1984, 48(4), 705–710 (in Russian)
  • [15] King A., Schofield A., Rationality of moduli of vector bundles on curves, Indag. Math. (N.S.), 1999, 10(4), 519–535
  • [16] Miyata T., Invariants of certain groups. I, Nagoya Math. J., 1971, 41, 69–73
  • [17] Perroud M., On the irreducible representations of the Lie algebra chain G 2 ⊃ A 2, J. Mathematical Phys., 1976, 17(11), 1998–2006
  • [18] Popov A.M., Irreducible semisimple linear Lie groups with finite stationary subgroups of general position, Funct. Anal. Appl., 1978, 12(2), 154–155
  • [19] Popov V.L., Classification of spinors in dimension fourteen, Trans. Moscow Math. Soc., 1980, 1, 181–232
  • [20] Popov V.L., Vinberg E.B., Invariant Theory, In: Algebraic Geometry IV, Encyclopaedia Math. Sci., 55, Springer, Berlin, 1994
  • [21] Saltman D., Lectures on Division Algebras, CBMS Regional Conf. Ser. in Math., 94, American Mathematical Society, Providence, 1999
  • [22] Schwarz G.W., Brion M., Théorie des Invariants et Géométrie des Variétés Quotients, Travaux en Cours, 61, Hermann Éditeurs des Sciences et des Arts, Paris, 2000
  • [23] Springer T.A., Veldkamp F.D., Octonions, Jordan Algebras and Exceptional Groups, Springer Monogr. Math., Springer, Berlin, 2000
  • [24] Van den Bergh M., The center of the generic division algebra, J. Algebra, 1989, 127(1), 106–126
  • [25] Vinberg E.B., The Weyl group of a graded Lie algebra, Math. USSR-Izv., 1976, 10(3), 463–495
  • [26] Wallach N., Yacobi O., A multiplicity formula for tensor products of SL2 modules and an explicit Sp2n to Sp2n−2×Sp2 branching formula, In: Symmetry in Mathematics and Physics, Contemp. Math., 490, American Mathematical Society, Providence, 2009, 151–155
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