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- W2697560692 abstract "We study singular rational curves in projective space, deducing conditions on their parametrizations from the value semigroups $sss$ of their singularities. In particular, we prove that a natural heuristic for the codimension of the space of nondegenerate rational curves of arithmetic genus $g>0$ and degree $d$ in $mb{P}^n$, viewed as a subspace of all degree-$d$ rational curves in $mb{P}^n$, holds whenever $g$ is small. On the other hand, we show that this heuristic fails in general, by exhibiting an infinite family of examples of Severi-type varieties of rational curves containing excess components of dimension strictly larger than the space of $g$-nodal rational curves." @default.
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- W2697560692 date "2015-11-26" @default.
- W2697560692 modified "2023-09-27" @default.
- W2697560692 title "Dimension counts for singular rational curves via semigroups" @default.
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