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A Genus 43 Curve - Differentials

Mar 3, 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 space of holomorphic differentials on XX is spanned by the following 4343 differentials:

y2/(11y10224y66xy2+768y2)y3/(11y10224y66xy2+768y2)y4/(11y10224y66xy2+768y2)y5/(11y10224y66xy2+768y2)y6/(11y10224y66xy2+768y2)y7/(11y10224y66xy2+768y2)y8/(11y10224y66xy2+768y2)y9/(11y10224y66xy2+768y2)xy2/(11y10224y66xy2+768y2)xy3/(11y10224y66xy2+768y2)xy4/(11y10224y66xy2+768y2)xy5/(11y10224y66xy2+768y2)xy6/(11y10224y66xy2+768y2)xy7/(11y10224y66xy2+768y2)xy8/(11y10224y66xy2+768y2)x2y2/(11y10224y66xy2+768y2)x2y3/(11y10224y66xy2+768y2)x2y4/(11y10224y66xy2+768y2)x2y5/(11y10224y66xy2+768y2)x2y6/(11y10224y66xy2+768y2)x2y7/(11y10224y66xy2+768y2)x3y2/(11y10224y66xy2+768y2)x3y3/(11y10224y66xy2+768y2)x3y4/(11y10224y66xy2+768y2)x3y5/(11y10224y66xy2+768y2)x3y6/(11y10224y66xy2+768y2)x4y/(11y10224y66xy2+768y2)x4y2/(11y10224y66xy2+768y2)x4y3/(11y10224y66xy2+768y2)x4y4/(11y10224y66xy2+768y2)x4y5/(11y10224y66xy2+768y2)x5y/(11y10224y66xy2+768y2)x5y2/(11y10224y66xy2+768y2)x5y3/(11y10224y66xy2+768y2)x5y4/(11y10224y66xy2+768y2)x6y/(11y10224y66xy2+768y2)x6y2/(11y10224y66xy2+768y2)x6y3/(11y10224y66xy2+768y2)x7y/(11y10224y66xy2+768y2)x7y2/(11y10224y66xy2+768y2)x8/(11y10224y66xy2+768y2)x8y/(11y10224y66xy2+768y2)x9/(11y10224y66xy2+768y2) \begin{aligned} y^2/(11y^{10} - 224y^6 - 6xy^2 + 768y^2) \\ y^3/(11y^{10} - 224y^6 - 6xy^2 + 768y^2) \\ y^4/(11y^{10} - 224y^6 - 6xy^2 + 768y^2) \\ y^5/(11y^{10} - 224y^6 - 6xy^2 + 768y^2) \\ y^6/(11y^{10} - 224y^6 - 6xy^2 + 768y^2) \\ y^7/(11y^{10} - 224y^6 - 6xy^2 + 768y^2) \\ y^8/(11y^{10} - 224y^6 - 6xy^2 + 768y^2) \\ y^9/(11y^{10} - 224y^6 - 6xy^2 + 768y^2) \\ xy^2/(11y^{10} - 224y^6 - 6xy^2 + 768y^2) \\ xy^3/(11y^{10} - 224y^6 - 6xy^2 + 768y^2) \\ xy^4/(11y^{10} - 224y^6 - 6xy^2 + 768y^2) \\ xy^5/(11y^{10} - 224y^6 - 6xy^2 + 768y^2) \\ xy^6/(11y^{10} - 224y^6 - 6xy^2 + 768y^2) \\ xy^7/(11y^{10} - 224y^6 - 6xy^2 + 768y^2) \\ xy^8/(11y^{10} - 224y^6 - 6xy^2 + 768y^2) \\ x^2y^2/(11y^{10} - 224y^6 - 6xy^2 + 768y^2) \\ x^2y^3/(11y^{10} - 224y^6 - 6xy^2 + 768y^2)\\ x^2y^4/(11y^{10} - 224y^6 - 6xy^2 + 768y^2)\\ x^2y^5/(11y^{10} - 224y^6 - 6xy^2 + 768y^2)\\ x^2y^6/(11y^{10} - 224y^6 - 6xy^2 + 768y^2)\\ x^2y^7/(11y^{10} - 224y^6 - 6xy^2 + 768y^2)\\ x^3y^2/(11y^{10} - 224y^6 - 6xy^2 + 768y^2)\\ x^3y^3/(11y^{10} - 224y^6 - 6xy^2 + 768y^2)\\ x^3y^4/(11y^{10} - 224y^6 - 6xy^2 + 768y^2)\\ x^3y^5/(11y^{10} - 224y^6 - 6xy^2 + 768y^2)\\ x^3y^6/(11y^{10} - 224y^6 - 6xy^2 + 768y^2)\\ x^4y/(11y^{10} - 224y^6 - 6xy^2 + 768y^2)\\ x^4y^2/(11y^{10} - 224y^6 - 6xy^2 + 768y^2)\\ x^4y^3/(11y^{10} - 224y^6 - 6xy^2 + 768y^2)\\ x^4y^4/(11y^{10} - 224y^6 - 6xy^2 + 768y^2)\\ x^4y^5/(11y^{10} - 224y^6 - 6xy^2 + 768y^2)\\ x^5y/(11y^{10} - 224y^6 - 6xy^2 + 768y^2)\\ x^5y^2/(11y^{10} - 224y^6 - 6xy^2 + 768y^2)\\ x^5y^3/(11y^{10} - 224y^6 - 6xy^2 + 768y^2)\\ x^5y^4/(11y^{10} - 224y^6 - 6xy^2 + 768y^2)\\ x^6y/(11y^{10} - 224y^6 - 6xy^2 + 768y^2)\\ x^6y^2/(11y^{10} - 224y^6 - 6xy^2 + 768y^2)\\ x^6y^3/(11y^{10} - 224y^6 - 6xy^2 + 768y^2)\\ x^7y/(11y^{10} - 224y^6 - 6xy^2 + 768y^2)\\ x^7y^2/(11y^{10} - 224y^6 - 6xy^2 + 768y^2)\\ x^8/(11y^{10} - 224y^6 - 6xy^2 + 768y^2)\\ x^8y/(11y^{10} - 224y^6 - 6xy^2 + 768y^2)\\ x^9/(11y^{10} - 224y^6 - 6xy^2 + 768y^2)\\ \end{aligned}