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arXiv · 2510.04275

The Evolution of Enumerative Geometry: A Narrative from Classical Problems to Enriched Invariants

Candace Bethea·Thomas Brazelton
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Abstract

Enumerative geometry, the art and science of counting geometric objects satisfying geometric conditions, has seen a resurgence of activity in recent years due to an influx of new techniques that allow for enriched computations. This paper offers a historical survey of enumerative geometry, starting with its classical origins and real counterparts, to new advances in quadratic enrichment. We include a brief survey of the paradigm shift initiated by Gromov-Witten theory, whose impact can be seen in recent results in quadratically enriched enumerative geometry. Finally, we conclude with a brief overview of emerging directions including random and equivariant enumerative geometry.

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Candace Bethea, Thomas Brazelton. 2025-10-05. The Evolution of Enumerative Geometry: A Narrative from Classical Problems to Enriched Invariants. https://arxiv.org/abs/2510.04275

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