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John Voight : Computing with Hilbert modular surfaces

Hilbert modular surfaces are 2-dimensional analogues of modular curves, parametrizing polarized abelian surfaces with endomorphism and level structure. Modular curves are stratified by genus, and canonical equations for modular curves are obtained from the graded ring of modular forms. Similar to how curves are stratified by genus, surfaces are organized by their numerical invariants; the Enriques-Kodaira classification organizes smooth surfaces by Kodaira dimension, Hodge numbers, and Chern numbers. In this talk, we explain how to compute these invariants and equations for certain Hilbert modular surfaces. This is joint work with Eran Assaf, Angie Babei, Ben Breen, Sara Chari, Edgar Costa, Juanita Duque-Rosero, Alex Horawa, Jean Kieffer, Avi Kulkarni, Grant Molnar, Abhijit S. Mudigonda, Michael Musty, Sam Schiavone, Shikhin Sethi, and Samuel Tripp.

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