Enumeration of non-nodal real plane rational curves
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2022
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913402042974208 |
|---|---|
| author | Shustin, Eugenii |
| author_facet | Shustin, Eugenii |
| contents | Welschinger invariants enumerate real nodal rational curves in the plane or in another real rational surface. We analyze the existence of similar enumerative invariants that count real rational plane curves having prescribed non-nodal singularities and passing through a generic conjugation-invariant configuration of appropriately many points in the plane. We show that an invariant like this is unique: it enumerates real rational three-cuspidal quartics that pass through generically chosen four pairs of complex conjugate points. Consequently, we show that through any generic configuration of four pairs of complex conjugate points, one can always trace a pair of real rational three-cuspidal quartics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_05932 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Enumeration of non-nodal real plane rational curves Shustin, Eugenii Algebraic Geometry 14N10, 14H15, 14H20, 14P05 Welschinger invariants enumerate real nodal rational curves in the plane or in another real rational surface. We analyze the existence of similar enumerative invariants that count real rational plane curves having prescribed non-nodal singularities and passing through a generic conjugation-invariant configuration of appropriately many points in the plane. We show that an invariant like this is unique: it enumerates real rational three-cuspidal quartics that pass through generically chosen four pairs of complex conjugate points. Consequently, we show that through any generic configuration of four pairs of complex conjugate points, one can always trace a pair of real rational three-cuspidal quartics. |
| title | Enumeration of non-nodal real plane rational curves |
| topic | Algebraic Geometry 14N10, 14H15, 14H20, 14P05 |
| url | https://arxiv.org/abs/2209.05932 |