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- W2962904443 abstract "We study the structure of collections of algebraic curves in three dimensions that have many curve-curve incidences. In particular, let $k$ be a field and let ${cal L}$ be a collection of $n$ space curves in $k^3$, with $nll ({rm char}(k))^2$ or ${rm char}(k)=0$. Then either (a) there are at most $O(n^{3/2})$ points in $k^3$ hit by at least two curves, or (b) at least $Omega(n^{1/2})$ curves from ${cal L}$ must lie on a bounded-degree surface, and many of the curves must form two ``rulings'' of this surface. We also develop several new tools including a generalization of the classical flecnode polynomial of Salmon and new algebraic techniques for dealing with this generalized flecnode polynomial." @default.
- W2962904443 created "2019-07-30" @default.
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- W2962904443 date "2018-01-01" @default.
- W2962904443 modified "2023-10-17" @default.
- W2962904443 title "Algebraic curves, rich points, and doubly-ruled surfaces" @default.
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- W2962904443 doi "https://doi.org/10.1353/ajm.2018.0028" @default.
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