Suppose $X$ is an algebraic variety, defined by the zero set of a known polynomial and furthermore that $X$ is also a Riemann surface.
I would greatly appreciate any resource recommendations that outline how one can evaluate the period matrix $\Omega$ of $X$. I know there is a text, Computational Approach to Riemann Surfaces which outlines (among other things) how to obtain numerical approximations but I would be more interested in how an exact form of $\Omega$ is obtained.
As a physicist, I would also favour approaches which deal with 'common' tools from differential and algebraic geometry (I realise this is somewhat subjective), rather than say a specific subtopic like Arakelov theory.
My own efforts have not yielded many results, other than the book I mentioned. Bolza's paper, On Binary Sextics with Linear Transformations into Themselves demonstrates one explicit computation for the case of the Burnside curve, $y^2 = x(x^4-1)$.