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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.03342 |
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| _version_ | 1866914566339821568 |
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| author | Reda, Vincenzo |
| author_facet | Reda, Vincenzo |
| contents | Ardila and Brugallé conjectured that double tropical Welschinger invariants of Hirzebruch surfaces are piecewise quasipolynomial. In this work, we prove the conjecture holds in full generality, i.e. for toric surfaces corresponding to h-transverse polygons. Furthermore, we define new combinatorial Welschinger-type numbers for h-transverse polygons and show that they are likewise piecewise quasipolynomial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_03342 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the piecewise quasipolynomiality of double tropical Welschinger invariants Reda, Vincenzo Algebraic Geometry Combinatorics 14N10, 14T90 Ardila and Brugallé conjectured that double tropical Welschinger invariants of Hirzebruch surfaces are piecewise quasipolynomial. In this work, we prove the conjecture holds in full generality, i.e. for toric surfaces corresponding to h-transverse polygons. Furthermore, we define new combinatorial Welschinger-type numbers for h-transverse polygons and show that they are likewise piecewise quasipolynomial. |
| title | On the piecewise quasipolynomiality of double tropical Welschinger invariants |
| topic | Algebraic Geometry Combinatorics 14N10, 14T90 |
| url | https://arxiv.org/abs/2511.03342 |