On the quotient ring by diagonal invariants
نویسندگان
چکیده
منابع مشابه
On the Quotient Ring by Diagonal Invariants
For a finite Coxeter group, W , and its reflection representation h, we find the character and Hilbert series for a quotient ring of C[h⊕h∗] by an ideal containing the W–invariant polynomials without constant term. This confirms conjectures of Haiman.
متن کاملConjectures on the Quotient Ring by Diagonal Invariants
We formulate a series of conjectures (and a few theorems) on the quotient of the polynomial ring Q[Z1 xn, y1,.. . , yn] in two sets of variables by the ideal generated by all Sn invariant polynomials without constant term. The theory of the corresponding ring in a single set of variables X = { x 1 , . . . , xn} is classical. Introducing the second set of variables leads to a ring about which li...
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Notes: 1) The modular diagonal quotient surfaces as defined above may be viewed as a special case of the general diagonal quotient surfaces studied in Kani/Schanz[7]. 2) The inclusions of subsgroups {1} ≤ ∆αε ≤ G × G induce finite morphisms (both of degree m = |G|) YN Φ → ZN,ε Ψ → Y1 ' P × P. Moreover, by using Shimura’s canonical model X(N)/Q, it can be shown that all these varieties have cano...
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Let X be a smooth projective curve over C which admits a finite group G of automorphisms. Then G×G acts on the product surface Y = X ×X, and so for each subgroup H ≤ G×G, the quotient Z = H\Y is a normal algebraic surface. Here we shall restrict attention to the case that the subgroup H is the graph of a group automorphism α ∈ Aut(G) of G, i.e. H = ∆α = {(g, α(g)) : g ∈ G}; we propose to call t...
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The main objective of this paper is to analyze the geometry of the modular diagonal quotient surface ZN,ε = ∆ε\(X(N) × X(N)) which classifies pairs of elliptic curves E1 and E2 together with an isomorphism of “determinant ε” between their associated modular representations mod N . In particular, we calculate some of the numerical invariants of its minimal desingularization Z̃N,ε such as its Bett...
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ژورنال
عنوان ژورنال: Inventiones Mathematicae
سال: 2003
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s00222-003-0296-5