An arithmetic count of the lines meeting four lines in $\mathbf {P}^3$

  title={An arithmetic count of the lines meeting four lines in \$\mathbf \{P\}^3\$},
  author={P. Srinivasan and Kirsten Wickelgren},
  journal={arXiv: Algebraic Geometry},
We enrich the classical count that there are two complex lines meeting four lines in space to an equality of isomorphism classes of bilinear forms. For any field $k$, this enrichment counts the number of lines meeting four lines defined over $k$ in $\mathbb{P}^3_k$, with such lines weighted by their fields of definition together with information about the cross-ratio of the intersection points and spanning planes. We generalize this example to an infinite family of such enrichments, obtained… Expand
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