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Precise Constants in Bosonization Formulas on Riemann Surfaces. I
Bosonization Formulas Riemann Surfaces
2015/12/17
A computation of the constant appearing in the spin-1 bosonization formulais given. This constant relates Faltings’ delta invariant to the zeta-regularized determinant of the Laplace operator with res...
GLUING FORMULAS FOR DETERMINANTS OF DOLBEAULT LAPLACIANS ON RIEMANN SURFACES
Determinants of Laplace operators Riemann surfaces bosonization formulas
2015/12/17
We present gluing formulas for zeta regularized determinants of Dolbeault laplacians on Riemann surfaces. These are expressed in terms of determinants of associated operators on surfaces with boundary...
A Lower Bound for the Number of Group Actions on a Compact Riemann Surface
Riemann surface automorphism signature mapping class group
2011/9/14
Abstract: We prove that the number of distinct group actions on compact Riemann surfaces of a fixed genus $\sigma \geq 2$ is at least quadratic in $\sigma$. We do this through the introduction of a co...
A stellar proof of Hirzebruch-Riemann-Roch for toric varieties
Toric variety Chow ring cohomology
2011/8/24
Abstract: We give a simple proof of the Hirzebruch-Riemann-Roch theorem for smooth complete toric varieties, based on Ishida's result that the Todd genus of a smooth complete toric variety is one.
Harmonic analysis and the Riemann-Roch theorem
Harmonic analysis the Riemann-Roch theorem Algebraic Geometry
2011/8/23
Abstract: This paper is a continuation of papers: arXiv:0707.1766 [math.AG] and arXiv:0912.1577 [math.AG]. Using the two-dimensional Poisson formulas from these papers and two-dimensional adelic theor...
A Riemann theta function formula with its application to double periodic wave solutions of nonlinear equations
Riemann theta function Hirota's bilinear form nonlinear equations
2010/4/1
Based on a Riemann theta function and Hirota's bilinear form, a lucid and straightforward way is presented to explicitly construct double periodic wave solutions for both nonlinear differential and di...