K-moduli wall crossing for quasimaps to a projective variety
Abstract
We develop a modular wall crossing theory for quasimaps to a projective variety, allowing independent variation of the boundary coefficients and the quasimap weight. Building on the K-stability of quasimaps introduced by Hashizume and the first author, we construct projective moduli spaces in the stable, Calabi--Yau, and log Fano regimes, together with wall crossing morphisms. A central construction is the moduli theory of boundary polarized Calabi--Yau quasimaps, which retains an ample polarization at the numerically trivial locus and allows comparison with suitable perturbations toward the stable and log Fano regions. The stable theory applies in arbitrary genus, while the comparisons through the Calabi--Yau locus concern genus zero. For degree-one boundary divisors, the resulting framework relates weighted stable maps and quasimaps to Hassett spaces and GIT quotients of weighted points on ℙ1. In a companion paper, we apply this framework to give a modular interpolation between Miranda's GIT compactification of rational elliptic surfaces and the Baily--Borel compactification of an eight-dimensional ball quotient.
Related
- Log Calabi-Yau wall crossing for moduli of cubic surfaces
- K-Moduli Wall Crossing and Automorphic Forms for the Moduli Space of Rational Elliptic Surfaces
- Examples of descendent generating series for Pandharipande--Thomas stable pairs on smooth projective Fano threefolds via one-dimensional wall-crossing
- Equivariant compactifications of a unipotent group by a smooth projective horospherical variety of Picard number one
- Projective embedding of degenerating family of Kähler-Einstein manifolds with normal crossing limit
BibTeX
@misc{hattori2026kmoduli,
title = {{K-moduli wall crossing for quasimaps to a projective variety}},
author = {Masafumi Hattori and Yota Maeda},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10784},
eprint = {2610.10784},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10784},
}
RIS
TY - UNPB
TI - K-moduli wall crossing for quasimaps to a projective variety
AU - Masafumi Hattori
AU - Yota Maeda
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10784
UR - https://arxiv.org/abs/2610.10784
AB - We develop a modular wall crossing theory for quasimaps to a projective variety, allowing independent variation of the boundary coefficients and the quasimap weight. Building on the K-stability of quasimaps introduced by Hashizume and the first author, we construct projective moduli spaces in the stable, Calabi--Yau, and log Fano regimes, together with wall crossing morphisms. A central construction is the moduli theory of boundary polarized Calabi--Yau quasimaps, which retains an ample polarization at the numerically trivial locus and allows comparison with suitable perturbations toward the stable and log Fano regions. The stable theory applies in arbitrary genus, while the comparisons through the Calabi--Yau locus concern genus zero. For degree-one boundary divisors, the resulting framework relates weighted stable maps and quasimaps to Hassett spaces and GIT quotients of weighted points on ℙ^1. In a companion paper, we apply this framework to give a modular interpolation between Miranda's GIT compactification of rational elliptic surfaces and the Baily--Borel compactification of an eight-dimensional ball quotient.
ER -