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small typo in globalA1Degree doc
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JordyLopez27 committed Oct 31, 2023
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Expand Up @@ -13,7 +13,7 @@ document {
PARA{"The ",
TEX///$\mathbb{A}^1$///,
EM "-Brouwer degree",
" first defined by Morel [M12] is an algebrao-geometric enrichment of the classical topological Brouwer degree. Using the tools of motivic homotopy theory, one may associate to an endomorphism of affine space the isomorphism class of a symmetric bilinear form whose invariants encode geometric data about how the morphism transforms space."
" first defined by Morel [M12] is an algebro-geometric enrichment of the classical topological Brouwer degree. Using the tools of motivic homotopy theory, one may associate to an endomorphism of affine space the isomorphism class of a symmetric bilinear form whose invariants encode geometric data about how the morphism transforms space."
},
PARA{"Such an association appears in the work of Eisenbud-Levine [EL77] and Khimshiashvili [K77], wherein the authors develop a symmetric bilinear form whose signature computes the local degree of a smooth map of real manifolds in the case where the Jacobian may vanish on an affine chart. This was proven to agree with Morel's ", TEX///$\mathbb{A}^1$///, "-Brouwer degree in work of Kass and Wickelgren [KW19]. A similar production of a symmetric bilinear form is given by work of Scheja and Storch [SS76], which develops a symmetric bilinear form attached to a complete intersection. This was also shown to align with the ", TEX///$\mathbb{A}^1$///, "-Brouwer degree in [BW23]."},
PARA{"Following recent work of B. McKean and Pauli [BMP23], the ", TEX///$\mathbb{A}^1$///, "-Brouwer degree can be computed as a multivariate ", EM "Bezoutian bilinear form.", " The algorithms for producing such a form are developed here."},
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