PreprintCC BY 4.0arXiv
Enumerative geometry of conics and double covers on projective complete intersections
Abstract
We compare genus zero degree two Gromov--Witten invariants with the number of embedded conics on general projective complete intersections whose conic space has expected dimension zero. Their difference comes from double covers of lines. We compute this contribution as an integral of Chern classes over the Fano scheme of lines, using an explicit obstruction bundle on the compactified space of double covers.
Related
- Quantum index, Arnold-Rokhlin surfaces, and real enumerative geometry
- Large Order Enumerative Geometry, Black Holes and Black Rings
- K-stability and birational rigidity of Fano 3-fold weighted complete intersections
- Existence of weak Landau-Ginzburg models for weighted complete intersections
- Generic Triviality of Linear Automorphisms of Complete Intersections
BibTeX
@misc{hiep2026enumerative,
title = {{Enumerative geometry of conics and double covers on projective complete intersections}},
author = {Dang Tuan Hiep and Ha Thi Thao Tram},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04837},
eprint = {2611.04837},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04837},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Enumerative geometry of conics and double covers on projective complete intersections
AU - Dang Tuan Hiep
AU - Ha Thi Thao Tram
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04837
UR - https://arxiv.org/abs/2611.04837
AB - We compare genus zero degree two Gromov--Witten invariants with the number of embedded conics on general projective complete intersections whose conic space has expected dimension zero. Their difference comes from double covers of lines. We compute this contribution as an integral of Chern classes over the Fano scheme of lines, using an explicit obstruction bundle on the compactified space of double covers.
ER -