PreprintCC BY 4.0arXiv
Morphism spaces on low degree hypersurfaces
Abstract
For r> 2, we study the moduli space parameterising fixed degree morphisms ℙr→ X where X is a smooth hypersurface of low degree. More precisely, we prove the following result: let n≥ 2, e≥ 1 and X⊂ ℙn−1 a smooth degree d≥ 2 hypersurface over an algebraically closed field of characteristic zero or greater than d, then More(ℙr, X) is irreducible of the expected dimension if n> 2d(d−1)binomde+r−1r−1. Our result extends the result of Browning-Yamagishi for r=2 via multiblock Weyl differencing.
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BibTeX
@misc{mishra2026morphism,
title = {{Morphism spaces on low degree hypersurfaces}},
author = {Hrishabh Mishra},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20783},
eprint = {2609.20783},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20783},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Morphism spaces on low degree hypersurfaces
AU - Hrishabh Mishra
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20783
UR - https://arxiv.org/abs/2609.20783
AB - For r> 2, we study the moduli space parameterising fixed degree morphisms ℙ^r→ X where X is a smooth hypersurface of low degree. More precisely, we prove the following result: let n≥ 2, e≥ 1 and X⊂ ℙ^n−1 a smooth degree d≥ 2 hypersurface over an algebraically closed field of characteristic zero or greater than d, then Mor_e(ℙ^r, X) is irreducible of the expected dimension if n> 2^d(d−1)binomde+r−1r−1. Our result extends the result of Browning-Yamagishi for r=2 via multiblock Weyl differencing.
ER -