Math Resources
Some background material on moduli of curves:
"The Moduli Space of Curves and its Tautological Ring", Ravi Vakil. Notices of the AMS.
"Combinatorial aspects of the moduli space of curves", Angela Gibney. Lectures from the BRIDGES program.
"Moduli spaces of pointed rational curves", Renzo Cavalieri. Lectures from the Fields Institute program in Combinatorial Algebraic Geometry, 2016.
"A Calculus for the Moduli Space of Curves", Rahul Pandharipande, arXiv.
Some additional material on blowups (one of the more frequently requested basic topics on our background knowledge survey and frequently mentioned in the project proposals):
Section 12.4 of "Algebra & Geometry A first course in Varieties" by Emily Clader and Dustin Ross
Two lectures on blowups from Richard Borcherds's online algebraic geometry course: