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We study Deligne products for forgetful maps between moduli spaces of marked curves by offering a closed formula for tautological
line bundles associated to marked points. In particular, we show that the Deligne products for line bundles on the total spaces
corresponding to “forgotten” marked points are positive integral multiples of the Weil-Petersson bundles on the base moduli
spaces.
Partially supported by the Japan Society for the Promotion of Science. 相似文献
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Don Zagier 《Proceedings Mathematical Sciences》1994,104(1):57-75
In 1956, Rankin described which polynomials in the derivatives of modular forms are again modular forms, and in 1977, H Cohen
defined for eachn ≥ 0 a bilinear operation which assigns to two modular formsf andg of weightk andl a modular form [f, g]n of weightk +l + 2n. In the present paper we study these “Rankin-Cohen brackets” from two points of view. On the one hand we give various explanations
of their modularity and various algebraic relations among them by relating the modular form theory to the theories of theta
series, of Jacobi forms, and of pseudodifferential operators. In a different direction, we study the abstract algebraic structure
(“RC algebra”) consisting of a graded vector space together with a collection of bilinear operations [,]n of degree + 2n satisfying all of the axioms of the Rankin-Cohen brackets. Under certain hypotheses, these turn out to be
equivalent to commutative graded algebras together with a derivationS of degree 2 and an element Φ of degree 4, up to the equivalence relation (∂,Φ) ~ (∂ - ϕE, Φ - ϕ2 + ∂(ϕ)) where ϕ is an element of degree 2 andE is the Fuler operator (= multiplication by the degree).
Dedicated to the memory of Professor K G Ramanathan 相似文献
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We give a parametric family of quintic polynomials of the form x5 + ax + b (a, b ∈ ) with dihedral Galois group D5. Some properties of the fields defined by these polynomials are also described. 相似文献
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Jacobi forms and a certain space of modular forms 总被引:2,自引:0,他引:2
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Don Zagier 《Communications in Mathematical Physics》1992,147(1):199-210
Following Greenberg and others, we study a space with a collection of operatorsa(k) satisfying the q-mutator relationsa(l)a
(k)a(l)=
k,l
(corresponding forq=±1 to classical Bose and Fermi statistics). We show that then!×n! matrixA
n
(q) representing the scalar products ofn-particle states is positive definite for alln ifq lies between –1 and +1, so that the commutator relations have a Hilbert space representation in this case (this has also been proved by Fivel and by Bozejko and Speicher). We also give an explicit factorization ofA
n
(q) as a product of matrices of the form(1–q
jT)±1 with 1jn andT a permutation matrix. In particular,A
n
(q) is singular if and only ifq
M=1 for some integerM of the formk
2–k, 2kn. 相似文献