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Vector-Valued Modular Forms from the Mumford Form, Schottky-Igusa Form, Product of Thetanullwerte and the Amazing Klein Formula
Marco Matone, Roberto Volpato
Vector-valued Siegel modular forms are the natural generalization of the classical elliptic modular forms as seen by studying the cohomology of the universal abelian variety. We sh…
The Singular Locus of the Theta Divisor and Quadrics through a Canonical Curve
Marco Matone, Roberto Volpato
A section K on a genus g canonical curve C is identified as the key tool to prove new results on the geometry of the singular locus Theta_s of the theta divisor. The K divisor is c…
Determinantal Characterization of Canonical Curves and Combinatorial Theta Identities
Marco Matone, Roberto Volpato
We characterize genus g canonical curves by the vanishing of combinatorial products of g+1 determinants of Brill-Noether matrices. This also implies the characterization of canonic…
Linear relations among holomorphic quadratic differentials and induced Siegel's metric on M_g
Marco Matone, Roberto Volpato
We derive the explicit form of the (g-2)(g-3)/2 linearly independent relations among the products of pairs in a basis of holomorphic abelian differentials in the case of canonical…
Eigenfunctions of the Laplacian Acting on Degree Zero Bundles over Special Riemann Surfaces
Marco Matone
We find an infinite set of eigenfunctions for the Laplacian with respect to a flat metric with conical singularities and acting on degree zero bundles over special Riemann surfaces…