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math.AG2026
Derived supergeometry and perfect obstruction theories on algebraic superstacks
Ugo Bruzzo, Daniel Hernández Ruipérez, Emanuele Pavia +1
We develop a deformation-theoretic framework for algebraic superstacks and apply it to the construction of perfect obstruction theories on moduli spaces of stable supermaps. In ord…
math.AG2025
Foundations of superstack theory
Ugo Bruzzo, Daniel Hernández Ruipérez
In view of applications to the construction of moduli spaces of objects in algebraic supergeometry, we start a systematic study of stacks in that context. After defining a supersta…
math.AG2025
Moduli of stable supermaps
Ugo Bruzzo, Daniel Hernández Ruipérez
We review the notion of stable supermap from SUSY curves to a fixed target superscheme, and prove that when the target is (super)projective, stable supermaps are parameterized by a…