PreprintarXiv licencearXiv
Kappa Classes on the KSBA Space of Stable Toric Pairs
Abstract
We study kappa classes on the normalization of the main component of the Kollár--Shepherd-Barron--Alexeev(KSBA) moduli space of stable toric pairs. Using a toric model obtained by a lattice modification, we compute all kappa classes on the moduli space by giving a combinatorial formula for their intersection numbers with all torus-invariant cycles. In particular, we identify the first normalized kappa class with the GKZ polarization of the toric variety corresponding to the secondary polytope. For interval configurations, we also obtain a closed formula for all top intersection products of normalized kappa classes.
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BibTeX
@misc{han2026kappa,
title = {{Kappa Classes on the KSBA Space of Stable Toric Pairs}},
author = {Byeol Han},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08337},
eprint = {2611.08337},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08337},
}
RIS
TY - UNPB
TI - Kappa Classes on the KSBA Space of Stable Toric Pairs
AU - Byeol Han
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08337
UR - https://arxiv.org/abs/2611.08337
AB - We study kappa classes on the normalization of the main component of the Kollár--Shepherd-Barron--Alexeev(KSBA) moduli space of stable toric pairs. Using a toric model obtained by a lattice modification, we compute all kappa classes on the moduli space by giving a combinatorial formula for their intersection numbers with all torus-invariant cycles. In particular, we identify the first normalized kappa class with the GKZ polarization of the toric variety corresponding to the secondary polytope. For interval configurations, we also obtain a closed formula for all top intersection products of normalized kappa classes.
ER -