# Remodeling the B-Model

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We prove that the moduli space of plane curves of degree d is rational for all sufficiently large d.

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We investigate D = 4, N = 1 F theory models realized by type IIB string compactification on toric threefolds. Massless spectra, gauge symmetries, phase transitions associated with divisor contractions and flops, and nonperturbative superpotentials are analyzed using elementary toric methods.

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For two-dimensional toric varieties X, an analog of the Fubini-Studi form Ï‰0 is constructed together with the canonical form Ï‰ that is the kernel of an integral representation for holomorphic functions in d-circular domains in Cd connected with two-dimensional toric varieties X. This...

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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 ï¿½forgottenï¿½...

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Consider the moduli space of pairs (C,?) where C is a smooth compact complex curve of a given genus and ? is a holomorphic 1-form on C with a given list of multiplicities of zeroes. We describe connected components of this space. This classification is important in the study of dynamics of...

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We improve estimates for the distribution of primitive ?-roots of a composite modulus q yielding an asymptotic formula for the number of primitive ?-roots in any interval I of length | I| ï¿½ q 1/2+?. Similar results are obtained for the distribution of ordered pairs ( x, x -1) with x a...

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For the spaces Lp and C of periodic functions of many variables we establish general theorems connecting the saturation classes generated by approximation methods with similar classes for continuity moduli.

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We investigate the moduli space of complex structures on the Riemann sphere with marked points using signature formulas.

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In this paper, we study effective recursion formulae for computing intersection numbers of mixed and classes on moduli spaces of curves. By using the celebrated Wittenâ€“Kontsevich theorem, we generalize Mulaseâ€“Safnuk form of Mirzakhani's recursion and prove a recursion formula of...