17 citations · 36 across the 10 of their papers we have counts for
4 papers · 1 filter
Lifts, transfers, and degrees of univariate maps
Thomas Brazelton, Stephen McKean
One can compute the local -degree at points with separable residue field by base changing, working rationally, and post-composing with the field trace. We show that f…
Conics meeting eight lines over perfect fields
Cameron Darwin, Aygul Galimova, Miao Pam Gu +1
Over the complex numbers, there are 92 plane conics meeting 8 general lines in projective 3-space. Using the Euler class and local degree from motivic homotopy theory, we give an e…
Bézoutians and the -degree
Thomas Brazelton, Stephen McKean, Sabrina Pauli
We prove that both the local and global -degree of an endomorphism of affine space can be computed in terms of the multivariate Bézoutian. In particular, we show that…
Rational lines on smooth cubic surfaces
Stephen McKean
We prove that the enumerative geometry of lines on smooth cubic surfaces is governed by the arithmetic of the base field. In 1949, Segre proved that the number of lines on a smooth…