Complex Analysis and Riemann Surfaces - A Graduate Path to Algebraic Geometry

These lecture notes explicitly aim to bridge classical complex analysis → compact Riemann surfaces → algebraic geometry using a pragmatic learning strategy: “compute first, then abstract.” I am documenting them here as a reference for (1) structured self-study and (2) potential reading-group use.

Note: This post summarizes the authors’ stated scope and roadmap (from the abstract/metadata), not a full technical review of every chapter.

Citation / BibTeX

@misc{cho2026complex,
  title        = {Complex Analysis and Riemann Surfaces: A Graduate Path to Algebraic Geometry},
  author       = {Cho, Gunhee and Dongsong, Bae and Boo, Junhyuk and Jeon, Byungjoo and Ji, Yonghyun and Kim, Sumin and Kim, Namho and Kwak, Minseung and Jung, Hojae and Yoo, Hyunsoo and Yoon, Hyunmin},
  year         = {2026},
  eprint       = {2601.06868},
  archivePrefix= {arXiv},
  primaryClass = {math.CV},
  doi          = {10.48550/arXiv.2601.06868},
  url          = {https://arxiv.org/abs/2601.06868}
}