Homogeneous-rational manifolds and unique factorization

Manfred Steinsiek

Compositio Mathematica (1984)

  • Volume: 52, Issue: 2, page 221-229
  • ISSN: 0010-437X

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Steinsiek, Manfred. "Homogeneous-rational manifolds and unique factorization." Compositio Mathematica 52.2 (1984): 221-229. <http://eudml.org/doc/89662>.

@article{Steinsiek1984,
author = {Steinsiek, Manfred},
journal = {Compositio Mathematica},
keywords = {homogeneously minimal embedding; homogeneous rational manifold},
language = {eng},
number = {2},
pages = {221-229},
publisher = {Martinus Nijhoff Publishers},
title = {Homogeneous-rational manifolds and unique factorization},
url = {http://eudml.org/doc/89662},
volume = {52},
year = {1984},
}

TY - JOUR
AU - Steinsiek, Manfred
TI - Homogeneous-rational manifolds and unique factorization
JO - Compositio Mathematica
PY - 1984
PB - Martinus Nijhoff Publishers
VL - 52
IS - 2
SP - 221
EP - 229
LA - eng
KW - homogeneously minimal embedding; homogeneous rational manifold
UR - http://eudml.org/doc/89662
ER -

References

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  1. [1] A. Andreotti and P. Salmon: Anneli con unica decomponibilità in fattori primi ed un problema di intersezione complete. Monatshefte Math. Physik61 (1957) 97-142. Zbl0079.15002MR104662
  2. [2] A. Borel: Kählerian coset spaces of semi-simple Lie groups. Proc. Nat. Acad. Sci. USA40 (1954) 1147-1151. Zbl0058.16002MR77878
  3. [3] A. Borel and R. Remmert: Über kompakte homogene Kählersche Mannigfaltigkeiten. Math. Ann.145 (1962) 429-439. Zbl0111.18001MR145557
  4. [4] A. Borel and A. Weil: Représentations linéaires et espaces homogènes Kählériens des groupes de Lie compacts. Sém. Bourbaki1954, no. 100 (Exposé par J.-P. Serre). Zbl0121.16203
  5. [5] R. Bott: Homogeneous vector bundles. Ann. Math. (2) 66 (1957) 203-248. Zbl0094.35701MR89473
  6. [6] V.I. Danilov: The group of ideal classes of a completed ring. Math. USSR Sb.6 (1968) 493-500. Zbl0186.07302
  7. [7] R.M. Fossum: The divisor class group of a Krull domain. Erg. der Math.74, Springer (1973). Zbl0256.13001MR382254
  8. [8] M. Goto: On algebraic homogeneous spaces. Amer. J. Math.76 (1954) 811-818. Zbl0056.39803MR66396
  9. [9] P.A. Griffiths and J. Harris: Principles of algebraic geometry. New York: Wiley (1978). Zbl0408.14001MR507725
  10. [10] R. Hartshorne: Algebraic geometry. GTM 52, Springer (1977). Zbl0367.14001MR463157
  11. [11] M. Hochster: Grassmannians and their Schubert varieties are arithmetically Cohen-Macaulay. J. Algebra25 (1973) 40-57. Zbl0256.14024MR314833
  12. [12] M. Hochster and J.L. Roberts: Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay. Advances in Math.13 (1974) 115-175. Zbl0289.14010MR347810
  13. [13] J. Igusa: On the arithmetic normality of the Grassmann variety. Proc. Nat. Acad. Sci. USA40 (1954) 309-313. Zbl0055.39002MR61423
  14. [14] I. Kaplansky: Commutative rings. Boston: Allyn and Bacon (1970). Zbl0203.34601MR254021
  15. [15] M. Lazard: Groupes semi-simples: Structure de B et de G/B. Sém. Chevalley 1956-1958: Classification des groupes de Lie algébriques. Exposé 13. 
  16. [16] J. Lipman: Unique factorization in complete local rings. AMS Proc. Symp. Pure Math.29 (1975) 531-546. Zbl0306.13005MR374125
  17. [17] M. Murthy: A note on factorial rings. Arch. Math.15 (1964) 418-420. Zbl0123.03401MR173695
  18. [18] R. Remmert and T. Van De Ven: Über holomorphe Abbildungen projektiv-algebraischer Mannigfaltigkeiten auf komplexe Räume. Math. Ann.142 (1961) 453-486. Zbl0099.16403MR145556
  19. [19] R. Remmert and A. Van De Ven: Zur Funktionentheorie homogener komplexer Mannigfaltigkeiten. Topology2 (1963) 137-157. Zbl0122.08602MR148085
  20. [20] P. Samuel: Lectures on unique factorization domains. Tata Inst. Fund. Res., No. 30, Bombay (1964). Zbl0184.06601MR214579
  21. [21] F. Severi: Sulla varietà che rappresenta gli spazî subordinati di data dimensione, immersi in uno spazio lineare. Ann. di Mat. (3) 24 (1915) 89-120. Zbl45.0915.03JFM45.1379.05
  22. [22] M. Steinsiek: Über homogen-rationale Mannigfaltigkeiten. Schriftenr. Math. Inst. Univ. Münster, 2. Serie, Bd. 23 (1982). Zbl0491.32025MR673379
  23. [23] M. Steinsiek: Transformation groups on homogeneous-rational manifolds. Math. Ann.260 (1982) 423-435. Zbl0503.32017MR670191
  24. [24] J. Tits: Sur certaines classes d'espaces homogènes de groupes de Lie. Mém. Acad. Roy. Belg.29 (1955) 1-268. Zbl0067.12301MR76286
  25. [25] J. Tits: Espaces homogènes complexes compacts. Comment. Math. Helv.37 (1962/63) 111-120. Zbl0108.36302MR154299

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