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We propose a strategy to study the analytic structure of Feynman parameterintegrals where singularities of the integrand consist of rational irreduciblecomponents. At the core of this strategy is the identification of a selectedstratum of discontinuities induced from the integral, together with a geometricmethod for computing their singularities on the principal sheet. For integralsthat yield multiple polylogarithms we expect the data collected in thisstrategy to be sufficient for the construction of their symbols. We motivatethis analysis by the Aomoto polylogarithms, and further check its validity andillustrate technical details using examples with quadric integrandsingularities (which the one-loop Feynman integrals belong to). Generalizationsto higher-loop integrals are commented at the end.

Towards Analytic Structure of Feynman Parameter Integrals with Rational Curves