In his letter [Ser96], J.-P. Serre proves that the systems of Hecke eigenvalues given by modular forms (mod p) are the same as the ones given by locally constant functions A×B/B × → F̄p, where B is the endomorphism algebra of a supersingular elliptic curve. After giving a detailed exposition of Serre’s result, we prove that the systems of Hecke eigenvalues given by Siegel modular forms (mod p) o...

— In [22], the authors proved an explicit formula for the arithmetic intersection number (CM(K).G1) on the Siegel moduli space of abelian surfaces, under some assumptions on the quartic CM field K. These intersection numbers allow one to compute the denominators of Igusa class polynomials, which has important applications to the construction of genus 2 curves for use in cryptography. One of the...

We analyze CP symmetry in symplectic modular-invariant supersymmetric theories. show that for genus g\ge 3 g≥3 the definition of is unique, while two independent possibilities are allowed when g\le 2 display="inline">g</mm...

In this paper we study the cohomology of certain local systems on moduli spaces of principally polarized abelian surfaces with a level 2 structure that corresponds to prescribing a number of Weierstrass points in case the abelian surface is the Jacobian of a curve of genus 2. These moduli spaces are defined over Z[1/2] and we can calculate the trace of Frobenius on the alternating sum of the ét...

Abstract Let J g be the Jacobian locus and let P +1 Prym locus, in moduli space A of principally polarized abelian varieties dimension , for ≥ 7. We study extrinsic geometry ⊂ under inclusion provided by theory generalized introduced Beauville. More precisely, we address problem if certain geodesic curves, defined with respect to Siegel metric starting at a variety [ JC ] ∈ curve C M direction ...

Due to a peculiar behavior at the open string midpoint, loop diagrams in Schnabl gauge were expected to fail to produce the relevant closed string moduli. We find that closed string moduli are generated because the Riemann surfaces are built with slanted wedges: semi-infinite strips whose edges have parameterizations related by scaling. We examine in detail one-loop string diagrams and find tha...

A bstract We revisit the proposal that ensemble average over free boson CFTs in two dimensions — parameterized by Narain’s moduli space is dual to an exotic theory of gravity three dubbed U(1) gravity. consider flavored partition functions, where usual genus g function weighted Wilson lines coupled conserved currents these theories. These functions obey a heat equation which relates deformation...

WZW models live on a moduli space parameterized by current-current deformations. The defines an ensemble of conformal field theories, which generically have $N$ abelian conserved currents and central charge $c > N$. We calculate the average partition function show that it can be interpreted as sum over 3-manifolds. This suggests ensemble-averaged theory has holographic dual, generalizing recent...

In this paper we study the expressions of the superstring chiral measures for g ≤ 5. We obtain certain new expressions which are functions of higher powers of theta constants. For g = 3 we show that the measures can be written in terms of theta constants to the fourth power and for g = 4 in term of squares of theta constants. In both cases the forms Ξ (g) 8 [0 ] appearing in the expression of t...