A quadratically enriched count of lines on a smooth del Pezzo surface of degree 5

Chachay Victor

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arXiv · 2607.29194

A quadratically enriched count of lines on a smooth del Pezzo surface of degree 5

Chachay Victor

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Abstract

In this paper, we give an enriched count for the 10 lines on a smooth del Pezzo surface S of degree 5 as the quadratic degree of the Euler class of a locally free sheaf. To do this, we see S as a section of the quintic del Pezzo threefold V 5 and the lines on S as a sub-scheme of the P 2 of lines on V 5 . We then use some oriented Schubert calculus and Bott residue formula with N SL 2 -action to compute the degree of the Euler class.

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BibTeX RIS

Chachay Victor. 2026-07-31. A quadratically enriched count of lines on a smooth del Pezzo surface of degree 5. https://arxiv.org/abs/2607.29194

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