An arithmetic count of the lines meeting four lines in P3

Journal Article (Journal Article)

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 P3k, 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 using an Euler number in A1-homotopy theory. The classical counts are recovered by taking the rank of the bilinear forms.

Full Text

Duke Authors

Cited Authors

  • Srinivasan, P; Wickelgren, K

Published Date

  • May 1, 2021

Published In

Volume / Issue

  • 374 / 5

Start / End Page

  • 3427 - 3451

Electronic International Standard Serial Number (EISSN)

  • 1088-6850

International Standard Serial Number (ISSN)

  • 0002-9947

Digital Object Identifier (DOI)

  • 10.1090/tran/8307

Citation Source

  • Scopus