Cubic Surfaces and Borcherds Products
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چکیده
منابع مشابه
Grothendieck-riemann-roch and the Moduli of Enriques Surfaces
A (complex) Enriques surface is a projective smooth connected algebraic surface Y over C with H(Y,OY ) = H (Y,OY ) = (0), (Ω 2 Y ) ⊗ 2 ≃ OY but Ω 2 Y 6≃ OY ([CF]). In this note we give a short proof of the fact that the coarse moduli space of complex Enriques surfaces is quasi-affine. This was first shown by Borcherds [B] using the denominator function of a generalized Kac-Moody superalgebra (t...
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We give an introduction to the theory of Borcherds products and to some number theoretic and geometric applications. In particular, we discuss how the theory can be used to study the geometry of Hilbert modular surfaces.
متن کاملTwisted Borcherds Products on Hilbert Modular Surfaces and Their Cm Values
We construct a natural family of rational functions Ψ̃m on a Hilbert modular surface from the classical j-invariant and its Hecke translates. These functions are obtained by means of a multiplicative analogue of the Doi-Naganuma lifting and can be viewed as twisted Borcherds products. We then study when the value of Ψ̃m at a CM point associated to a non-biquadratic quartic CM field generates the ...
متن کاملZagier Duality for the Exponents of Borcherds Products for Hilbert Modular Forms
A certain sequence of weight 1/2 modular forms arises in the theory of Borcherds products for modular forms for SL2(Z). Zagier proved a family of identities between the coefficients of these weight 1/2 forms and a similar sequence of weight 3/2 modular forms, which interpolate traces of singular moduli. We obtain the analogous results for modular forms arising from Borcherds products for Hilber...
متن کاملNotes on Borcherds Products
These are the notes for a short course on Borcherds Products held in Aachen on 1st2nd August 2012. The lectures are intended for someone who does not know what a Borcherds product is, but does know what a modular form is. In preparing these notes I’ve used the following sources: [1, 2, 3, 4, 5]. All the correct statements in these notes are taken from those sources, and all the mistakes are my ...
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تاریخ انتشار 2007