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- W4287395013 abstract "Let $k$ be a field and let $text{GW}(k)$ be the Grothendieck-Witt ring of virtual non-degenerate symmetric bilinear forms over $k$. We develop methods for computing the quadratic Euler characteristic $chi(X/k)in text{GW}(k)$ for $X$ a smooth hypersurface in a projective space or a weighted projective space. We raise the question of a quadratic refinement of classical conductor formulas and find such a formula for the degeneration of a smooth hypersurface $X$ in $mathbb{P}^{n+1}$ to the cone over a smooth hyperplane section of $X$; we also find a similar formula in the weighted homogeneous case. We formulate a conjecture that generalizes these computations to similar types of degenerations. Finally, we give an interpretation of the quadratic conductor formulas in terms of Ayoub's nearby cycles functor." @default.
- W4287395013 created "2022-07-25" @default.
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- W4287395013 date "2021-01-02" @default.
- W4287395013 modified "2023-09-26" @default.
- W4287395013 title "Euler characteristics of homogeneous and weighted-homogeneous hypersurfaces" @default.
- W4287395013 doi "https://doi.org/10.48550/arxiv.2101.00482" @default.
- W4287395013 hasPublicationYear "2021" @default.
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