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A Genus 43 Curve - Riemann Matrix

Mar 9, 2016

Consider the genus 4343 Riemann surface XX obtained from the desingularization and compactification of the plane algebraic curve

C:f(x,y)=y3((y416)22x)x12. C: f(x,y) = y^3 \big((y^4 - 16)^2 - 2x\big) - x^{12}.

The Riemann matrix (normalized period matrix) of this curve is given by:

Genus 43 Riemann Matrix

(Click to expand.) This matrix is indeed symmetric and its imaginary part is positive definite.