Skip to main content
Log in

Toric varieties as spectra of homogeneous prime ideals

  • Original Paper
  • Published:
Geometriae Dedicata Aims and scope Submit manuscript

Abstract

We describe the construction of a class of toric varieties as spectra of homogeneous prime ideals.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. A’Campo-Neuen A., Hausen J. and Schröer S. (2002). Homogeneous coordinates and quotient presentations for toric varieties. Math. Nachrichten 246–247: 5–19

    Article  Google Scholar 

  2. Brenner, H., Schröer, S.: Ample families, multihomogeneous spectra, and algebraization of formal schemes. Preprint, (2000). math.AG/0012082

  3. Cox D.A. (1995). The homogeneous coordinate ring of a toric variety. J. Algebr. Geom. 4(1): 17–50

    MATH  Google Scholar 

  4. Eisenbud D., Musta̧ǎ M. and Stillman M. (2000). Cohomology on toric varieties and local cohomology with monomial supports. J. Symb. Comput. 29(4–5): 583–600

    Article  MATH  Google Scholar 

  5. Fulton, W.: Introduction to Toric Varieties. Princeton University Press (1993)

  6. Grothendieck A. and Dieudonné J.A. (1961). Eléments de Géométrie Algébrique II. Publ. Math. IHES 8: 5–222

    Google Scholar 

  7. Kajiwara T. (1998). The functor of a toric variety with enough invariant divisors. Tôhoku Math. J. 50: 139–157

    MATH  Google Scholar 

  8. Miyake, K., Oda, T.: Lectures on Torus Embeddings and Applications. Springer (1978)

  9. Newstead, P.E.: Lectures on Introduction to Moduli Problems and Orbit Spaces, volume 51 of Tata Institute of Fundamental Research Lectures on Mathematics and Physics. Springer (1978)

  10. Oda, T.: Convex Bodies and Algebraic Geometry, volume 15 of Ergebnisse der Mathematik und ihrer Grenzgebiete. Springer (1988)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Markus Perling.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Perling, M. Toric varieties as spectra of homogeneous prime ideals. Geom Dedicata 127, 121–129 (2007). https://doi.org/10.1007/s10711-007-9167-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10711-007-9167-3

Keywords

Mathematical Subject Classification (1991)

Navigation