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- Title
Interpolation of curves on Fano hypersurfaces.
- Authors
Ran, Ziv
- Abstract
On a general hypersurface of degree d ≤ n in ℙ n or ℙ n itself, we prove the existence of curves of any genus and high enough degree depending on the genus passing through the expected number t of general points or incident to a general collection of subvarieties of suitable codimensions. In some cases, we also show that the family of curves through t fixed points has general moduli as family of t -pointed curves. These results imply positivity of certain intersection numbers on Kontsevich spaces of stable maps. An arithmetical Appendix A by Chang describes the set of numerical characters (n , d , curve degree, genus) to which our results apply.
- Subjects
INTERSECTION numbers; INTERPOLATION; HYPERSURFACES
- Publication
Communications in Contemporary Mathematics, 2024, Vol 26, Issue 1, p1
- ISSN
0219-1997
- Publication type
Article
- DOI
10.1142/S0219199723500025