The homogeneous coordinate ring of a toric variety

By David A. Cox. 2013

1,036 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/959809cdaf9940385877873e42023f6282b381b6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Sam Payne
2. Jürgen Hausen
3. T. Panov
4. M. Masuda
5. Hendrik Suss
6. Yunfeng Jiang
7. V. Buchstaber
8. Jenia Tevelev

In Computational Theory and Mathematics

1. T. Panov
2. V. Buchstaber
3. Jenia Tevelev
4. Adam Van Tuyl
5. Alberto Zaffaroni
6. Gregory G. Smith
7. Sam Payne
8. M. Masuda

In Geometry and Topology

1. Marcos Mariño
2. Alberto Zaffaroni
3. A. Hanany
4. Sam Payne
5. C. Vafa
6. A. Klemm
7. Yang-Hui He
8. M. Masuda

Citations in the corpus

• Phases Of N=2 Theories In 1+1 Dimensions With Boundary (2008, background): “To summarise: the category of coherent sheaves in each phase is equivalent, as an abelian category, to the category of multi-graded R-modules modulo a particular set of torsion subcategories associated to ∆r. 188 This generalization of Serre’s construction was originally given by Cox [84] in the cas”
• Toric hyperkähler varieties (2002, background): “The equations which cut out the toric quiver variety Y (Q, θ) lie in the Cox homogeneous coordinate ring of the Lawrence toric manifold X(Q±, θ).”
• The orbifold Chow ring of toric Deligne-Mumford stacks (2003, background): “However, the Cohomological Crepant Resolution Conjecture itself is by no means easy to settle even in the toric case, since it is generally rather difficult to calculate the quantum cohomology of toric varieties.”
• Moduli of toric vector bundles (2007, background): “Another classification of equivariant quasicoherent sheaves on toric varieties, developed earlier by Cox [Cox95] and Mustaţǎ [Mus02], involves fine graded modules over the homogeneous coordinate ring.”
• Multigraded Hilbert schemes (2002, methodology): “With this notation, we have XΣa = A /aG, and we can identify S with the Cox homogeneous coordinate ring [8] of XΣa .”
• The Cox ring of an algebraic variety with torus action (2009, background): “Similarly to the toric case [7], the advantage of the combinatorial treatment is that the divisor class group is easily accessible via the defining data and thus one has a simple approach to the grading of the Cox ring.”
• F-theory on all toric hypersurface fibrations and its Higgs branches (2014, background): “Toric varieties are generalizations of weighted projective spaces [86]: to each integral point vk, k = 1, .”
• Cox Rings and Combinatorics II (2008, neutral): “ar X iv :0 80 1.”