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Stable reductive varieties I: Affine varieties

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References

  1. Alexeev, V.: Complete moduli in the presence of semiabelian group action. Ann. Math. 155, 611–708 (2002)

    Article  MathSciNet  Google Scholar 

  2. Alexeev, V., Brion, M.: Stable reductive varieties II: Projective case. Preprint. arXiv:math.AG/0207274. To appear in Adv. Math.

  3. Deligne, P., Mumford, D.: The irreducibility of the moduli space of curves of given genus. Publ. Math., Inst. Hautes Étud. Sci. 36, 75–110 (1969)

    Article  MathSciNet  Google Scholar 

  4. Fulton, W.: Introduction to Toric Varieties. Ann. Math. Stud. 131. Princeton: Princeton University Press 1993

  5. Grosshans, F.: Algebraic homogeneous spaces and invariant theory. Lect. Note Math. 1673. Heidelberg: Springer 1997

  6. Hartshorne, R.: Algebraic geometry. Grad. Texts Math. 52. New York, Heidelberg: Springer 1977

  7. Haiman, M., Sturmfels, B.: Multigraded Hilbert schemes. Preprint. arXiv:math.AG/0201271. To appear in J. Algebr. Geom.

  8. Knop, F.: The Luna-Vust Theory of Spherical Embeddings. In: Proceedings of the Hyderabad Conference on Algebraic Groups, 225–249. Madras: Manoj-Prakashan 1989

  9. Knop, F.: The asymptotic behavior of invariant collective motion. Invent. Math. 116, 309–328 (1994)

    Article  MathSciNet  Google Scholar 

  10. Luna, D.: Adhérences d’orbites et invariants. Invent. Math. 29, 231–238 (1975)

    Article  MathSciNet  Google Scholar 

  11. Mumford, D.: Geometric invariant theory. Third enlarged edn., Ergeb. Math. Grenzgeb. 34. Berlin: Springer 1994

  12. Namikawa, Y.: A new compactification of the Siegel space and degenerations of abelian varieties, I, II. Math. Ann. 221, 97–141, 201–241 (1976)

    Article  MathSciNet  Google Scholar 

  13. Popov, V.L.: Contractions of actions of reductive algebraic groups. Mat. Sb. 130, 310–334 (1986)

    MathSciNet  Google Scholar 

  14. Popov, V.L., Vinberg, E.B.: Invariant theory. Encyclopaedia of Mathematical Sciences 55. Berlin: Springer 1994

  15. Putcha, M.S.: Green’s relations on a connected algebraic monoid. Linear Multilinear Algebra 12, 205–214 (1982/83)

  16. Putcha, M.S.: Reductive groups and regular semigroups. Semigroup Forum 30, 253–261 (1984)

    Article  MathSciNet  Google Scholar 

  17. Putcha, M.S., Renner, L.E.: The system of idempotents and the lattice of \(\mathcal{J}\)-classes of reductive algebraic monoids. J. Algebra 116, 385–399 (1988)

    Article  MathSciNet  Google Scholar 

  18. Rittatore, A.: Algebraic monoids and group embeddings. Transform. Groups 3, 375–396 (1998)

    Article  MathSciNet  Google Scholar 

  19. Solomon, L.: An introduction to reductive monoids. In: Semigroups, formal languages and groups (York, 1993), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 466, 295–352. Dordrecht: Kluwer Acad. Publ. 1995

  20. Vinberg, E.B.: Complexity of actions of reductive groups. Funct. Anal. Appl. 20, 1–11 (1986)

    Article  MathSciNet  Google Scholar 

  21. Vinberg, E.B.: On reductive algebraic semigroups. In: Lie groups and Lie algebras: E.B. Dynkin’s Seminar, Am. Math. Soc. Transl. Ser. 2 169, 145–182 (1995)

    MathSciNet  Google Scholar 

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Correspondence to Valery Alexeev or Michel Brion.

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Alexeev, V., Brion, M. Stable reductive varieties I: Affine varieties. Invent. math. 157, 227–274 (2004). https://doi.org/10.1007/s00222-003-0347-y

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