• Corpus ID: 249191544

Regularized Integrals on Elliptic Curves and Holomorphic Anomaly Equations

  title={Regularized Integrals on Elliptic Curves and Holomorphic Anomaly Equations},
  author={Si Li and Jie Zhou},
We derive residue formulas for the regularized integrals (introduced in [LZ21]) on configuration spaces of elliptic curves. Based on these formulas, we prove that the regularized integrals satisfy holomorphic anomaly equations, providing a mathematical formulation of the so-called contact term singularities. We also discuss residue formulas for the ordered A -cycle integrals and establish their relations with those for the regularized integrals. 



Regularized Integrals on Riemann Surfaces and Modular Forms

  • Si LiJie Zhou
  • Mathematics
    Communications in Mathematical Physics
  • 2021
We introduce a simple procedure to integrate differential forms with arbitrary holomorphic poles on Riemann surfaces. It gives rise to an intrinsic regularization of such singular integrals in terms

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