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Abstract We determine the cones of effective and nef divisors on the toroidal compactification of the ball quotient model of the moduli space of complex cubic surfaces with a chosen line. From this we also compute the corresponding cones for the moduli space of unmarked cubic surfaces. 

A<sc>bstract</sc> We present a complete computation of superstring scattering amplitudes at tree level, for the case of Neveu-Schwarz insertions. Mathematically, this is to say that we determine explicitly the superstring measure on the moduli space$$ {\mathcal{M}}_{0,n,0} $$ $M_{0,n,0}$of super Riemann surfaces of genus zero withn≥ 3 Neveu-Schwarz punctures. While, of course, an expression for the measure was previously known, we do this from first principles, using the canonically defined super Mumford isomorphism [1]. We thus determine the scattering amplitudes, explicitly in the global coordinates on$$ {\mathcal{M}}_{0,n,0} $$ $M_{0,n,0}$, without the need for picture changing operators or ghosts, and are also able to determine canonically the value of the coupling constant. Our computation should be viewed as a step towards performing similar analysis on$$ {\mathcal{M}}_{0,0,n} $$ $M_{0,0,n}$, to derive explicit tree-level scattering amplitudes with Ramond insertions. 

Abstract We study the cone of moving divisors on the moduli space $${\mathcal{A}}_{g}$$ of principally polarized abelian varieties. Partly motivated by the generalized Rankin–Cohen bracket, we construct a non-linear holomorphic differential operator that sends Siegel modular forms to Siegel modular forms, and we apply it to produce new modular forms. Our construction recovers the known divisors of minimal moving slope on $${\mathcal{A}}_{g}$$ for $$g\leq 4$$, and gives an explicit upper bound for the moving slope of $${\mathcal{A}}_{5}$$ and a conjectural upper bound for the moving slope of $${\mathcal{A}}_{6}$$.