The Evolution of Enumerative Geometry: A Narrative from Classical Problems to Enriched Invariants
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909825748697088 |
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| author | Bethea, Candace Brazelton, Thomas |
| author_facet | Bethea, Candace Brazelton, Thomas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04275 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Evolution of Enumerative Geometry: A Narrative from Classical Problems to Enriched Invariants Bethea, Candace Brazelton, Thomas Algebraic Geometry Combinatorics History and Overview 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. |
| title | The Evolution of Enumerative Geometry: A Narrative from Classical Problems to Enriched Invariants |
| topic | Algebraic Geometry Combinatorics History and Overview |
| url | https://arxiv.org/abs/2510.04275 |