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math.AG2024
Bitangents to symmetric quartics
Candace Bethea, Thomas Brazelton
Recall that a non-singular planar quartic is a canonically embedded non-hyperelliptic curve of genus three. We say such a curve is symmetric if it admits non-trivial automorphisms.…
math.AT2024
There is no Cazanave's Theorem for punctured affine space
Thomas Brazelton, William Hornslien
In his thesis, Cazanave proved that the set of naive -homotopy classes of endomorphisms of the projective line admits a monoid structure whose group completion is gen…
math.AG2024
Monodromy in the space of symmetric cubic surfaces with a line
Thomas Brazelton, Sidhanth Raman
We explore the enumerative problem of finding lines on cubic surfaces defined by symmetric polynomials. We prove that the moduli space of symmetric cubic surfaces is an arithmetic…