## An arithmetic count of the lines meeting four lines in P^{3}

Publication
, Journal Article

Srinivasan, P; Wickelgren, K

Published in: Transactions of the American Mathematical Society

May 1, 2021

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.

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## Published In

Transactions of the American Mathematical Society

## DOI

## EISSN

1088-6850

## ISSN

0002-9947

## Publication Date

May 1, 2021

## Volume

374

## Issue

5

## Start / End Page

3427 / 3451

## Related Subject Headings

- General Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics

### Citation

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Srinivasan, P., & Wickelgren, K. (2021). An arithmetic count of the lines meeting four lines in P

^{3}.*Transactions of the American Mathematical Society*,*374*(5), 3427–3451. https://doi.org/10.1090/tran/8307Srinivasan, P., and K. Wickelgren. “An arithmetic count of the lines meeting four lines in P

^{3}.”*Transactions of the American Mathematical Society*374, no. 5 (May 1, 2021): 3427–51. https://doi.org/10.1090/tran/8307.Srinivasan P, Wickelgren K. An arithmetic count of the lines meeting four lines in P

^{3}. Transactions of the American Mathematical Society. 2021 May 1;374(5):3427–51.Srinivasan, P., and K. Wickelgren. “An arithmetic count of the lines meeting four lines in P

^{3}.”*Transactions of the American Mathematical Society*, vol. 374, no. 5, May 2021, pp. 3427–51.*Scopus*, doi:10.1090/tran/8307.Srinivasan P, Wickelgren K. An arithmetic count of the lines meeting four lines in P

^{3}. Transactions of the American Mathematical Society. 2021 May 1;374(5):3427–3451.## Published In

Transactions of the American Mathematical Society

## DOI

## EISSN

1088-6850

## ISSN

0002-9947

## Publication Date

May 1, 2021

## Volume

374

## Issue

5

## Start / End Page

3427 / 3451

## Related Subject Headings

- General Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics