PreprintCC BY 4.0HAL
Algebraic ellipticity of quartic double spaces
Abstract
We prove that every smooth quartic double n-fold, n≥2, over an algebraically closed field of characteristic zero is algebraically elliptic in Gromov's sense. In particular, every smooth quartic double solid is algebraically elliptic, which answers Question~4.28 in \cite{Zai}. We also prove that removing any closed subset of codimension at least two preserves algebraic ellipticity for smooth quartic double spaces and smooth cubic hypersurfaces of dimension at least two.
Related
- Algebraic ellipticity of double covers of (P1)3
- A Sarkisov Involution from a Rational Cubic Curve on a Quartic Double Solid
- Betti bounds for spaces of curves on varieties and Manin's conjecture for quartic del Pezzo surfaces
- Algebraic hyperbolicity of very general hypersurfaces in projective spaces
- Maximality and configuration spaces on real algebraic curves
BibTeX
@misc{dvorsky2026algebraic,
title = {{Algebraic ellipticity of quartic double spaces}},
author = {Alexander Dvorsky and Shulim Kaliman and M Zaidenberg},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07260},
eprint = {2610.07260},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05843371v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Algebraic ellipticity of quartic double spaces
AU - Alexander Dvorsky
AU - Shulim Kaliman
AU - M Zaidenberg
PY - 2026
DA - 2026/10/05
PB - HAL
DO - 10.48550/arxiv.2610.07260
UR - https://hal.science/hal-05843371v1
AB - We prove that every smooth quartic double n-fold, n≥2, over an algebraically closed field of characteristic zero is algebraically elliptic in Gromov's sense. In particular, every smooth quartic double solid is algebraically elliptic, which answers Question~4.28 in \cite{Zai}. We also prove that removing any closed subset of codimension at least two preserves algebraic ellipticity for smooth quartic double spaces and smooth cubic hypersurfaces of dimension at least two.
ER -