{"ID":23664234,"CreatedAt":"2026-09-18T08:14:42.696445972Z","UpdatedAt":"2026-09-18T08:14:42.696445972Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.20783","arxiv_id":"2609.20783","title":"Morphism spaces on low degree hypersurfaces","abstract":"For $r\u003e 2$, we study the moduli space parameterising fixed degree morphisms $\\mathbb P^r\\to X$ where $X$ is a smooth hypersurface of low degree. More precisely, we prove the following result: let $n\\geq 2, e\\geq 1$ and $X\\subset \\mathbb P^{n-1}$ a smooth degree $d\\geq 2$ hypersurface over an algebraically closed field of characteristic zero or greater than $d$, then $\\mathrm{Mor}_e(\\mathbb P^r, X)$ is irreducible of the expected dimension if \\[ n\u003e 2^d(d-1)\\binom{de+r-1}{r-1}. \\] Our result extends the result of Browning-Yamagishi for $r=2$ via multiblock Weyl differencing.","short_abstract":"For $r\u003e 2$, we study the moduli space parameterising fixed degree morphisms $\\mathbb P^r\\to X$ where $X$ is a smooth hypersurface of low degree. More precisely, we prove the following result: let $n\\geq 2, e\\geq 1$ and $X\\subset \\mathbb P^{n-1}$ a smooth degree $d\\geq 2$ hypersurface over an algebraically closed field...","url_abs":"https://arxiv.org/abs/2609.20783","url_pdf":"https://arxiv.org/pdf/2609.20783v1","authors":"[\"Hrishabh Mishra\"]","published":"2026-09-17T17:51:54Z","proceeding":"math.AG","tasks":"[\"math.AG\",\"math.NT\"]","methods":"[]","has_code":false}