### Citations

2872 | Algebraic Geometry, - Hartshorne - 1977 |

119 | Geometric invariant theory, volume 34 of Ergebnisse der Mathematik und ihrer Grenzgebiete (2 - Mumford, Fogarty, et al. - 1994 |

99 | Gröbner geometry of Schubert polynomials
- Knutson, Miller
- 2005
(Show Context)
Citation Context ...e cocycle condition satisfied by ρ is then taken to be the usual cocycle condition defining any action. 4. From Multigraded modules to Torus equivariant sheaves As stated in [MS05, Chapter 8], and in =-=[KM05]-=-, Zd graded k[x] modules correspond to torus equivariant coherent sheaves. To avoid introducing the equivariant theory of a torus times a finite abelian group, hereafter all gradings are positive, and... |

45 |
Combinatorial commutative algebra, volume 227.
- Miller, Sturmfels
- 2005
(Show Context)
Citation Context ... Z4-graded module k[Y ] as, H(k[Y ], t) = ∑ a∈Z4 dimk(Ma)t a. More specifically, we have, H(k[Y ], t) = ∑ i=0 ( t4 t1 )i = 1 1− t4 t1 Since, the grading induced by the degree function deg is positive =-=[MS05]-=-, one may compute the Kpolynomial of k[Y ] as the unique numerator satisfying, H(k[Y ], t) = K(Γ; t)( 1− t4 t1 )( 1− t2 t3 ) (1 − t−21 ) . From our computation of the Hilbert series it follows immedia... |

31 | Equivariant K-theory, Inst. Hautes Etudes Sci. - Segal - 1968 |

15 | Schubert Classes in the Equivariant K-Theory and Equivariant
- Kreiman
(Show Context)
Citation Context ... K-polynomials, in the special (and in a sense, more traditional) case that the latter appear as certain numerators in the corresponding Hilbert Series. Below, we have expanded on an example found in =-=[Kre05]-=-. Example. Let X = k3, and T = C4 be the standard torus in GL4(C). We use xi to denote the standard coordinate functions on C3. Consider the following action of T on X, (x1, x2, x3) (t1,...,t4) −→ ( t... |

13 | Algebraic K-theory and its applications, volume 147 of Graduate Texts in Mathematics - Rosenberg - 1994 |

11 | On positivity in T -equivariant K-theory of flag varieties - Graham, Kumar |

8 |
Equivariant K-theory
- Merkurjev
- 2005
(Show Context)
Citation Context ...eld F. A variety X over F is called a G-variety if an action morphism θ : G ×X → X of the group G on X is given, which satisfies the usual associative and unital identities for an action. Definition. =-=[Mer05]-=-A G-module M over X is a quasi-coherent OX module together with an isomorphism of OG×X-modules ρ = ρM : θ ∗(M)→ p∗2(M), satisfying the cocycle condition p∗23(ρ) ◦ (idG × θ) ∗(ρ) = (m× idX) ∗(ρ). Above... |

7 | The K-book: an introduction to algebraic K-theory, http://math.rutgers. edu/~weibel/Kbook.html - Weibel |