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A Genus 43 Curve - Differentials
Mar 3, 2016
Consider the genus 43 Riemann surface X obtained from the desingularization
and compactification of the plane algebraic curve
C:f(x,y)=y3((y4−16)2−2x)−x12.
The space of holomorphic differentials on X is spanned by the following 43
differentials:
y2/(11y10−224y6−6xy2+768y2)y3/(11y10−224y6−6xy2+768y2)y4/(11y10−224y6−6xy2+768y2)y5/(11y10−224y6−6xy2+768y2)y6/(11y10−224y6−6xy2+768y2)y7/(11y10−224y6−6xy2+768y2)y8/(11y10−224y6−6xy2+768y2)y9/(11y10−224y6−6xy2+768y2)xy2/(11y10−224y6−6xy2+768y2)xy3/(11y10−224y6−6xy2+768y2)xy4/(11y10−224y6−6xy2+768y2)xy5/(11y10−224y6−6xy2+768y2)xy6/(11y10−224y6−6xy2+768y2)xy7/(11y10−224y6−6xy2+768y2)xy8/(11y10−224y6−6xy2+768y2)x2y2/(11y10−224y6−6xy2+768y2)x2y3/(11y10−224y6−6xy2+768y2)x2y4/(11y10−224y6−6xy2+768y2)x2y5/(11y10−224y6−6xy2+768y2)x2y6/(11y10−224y6−6xy2+768y2)x2y7/(11y10−224y6−6xy2+768y2)x3y2/(11y10−224y6−6xy2+768y2)x3y3/(11y10−224y6−6xy2+768y2)x3y4/(11y10−224y6−6xy2+768y2)x3y5/(11y10−224y6−6xy2+768y2)x3y6/(11y10−224y6−6xy2+768y2)x4y/(11y10−224y6−6xy2+768y2)x4y2/(11y10−224y6−6xy2+768y2)x4y3/(11y10−224y6−6xy2+768y2)x4y4/(11y10−224y6−6xy2+768y2)x4y5/(11y10−224y6−6xy2+768y2)x5y/(11y10−224y6−6xy2+768y2)x5y2/(11y10−224y6−6xy2+768y2)x5y3/(11y10−224y6−6xy2+768y2)x5y4/(11y10−224y6−6xy2+768y2)x6y/(11y10−224y6−6xy2+768y2)x6y2/(11y10−224y6−6xy2+768y2)x6y3/(11y10−224y6−6xy2+768y2)x7y/(11y10−224y6−6xy2+768y2)x7y2/(11y10−224y6−6xy2+768y2)x8/(11y10−224y6−6xy2+768y2)x8y/(11y10−224y6−6xy2+768y2)x9/(11y10−224y6−6xy2+768y2)