Point Corrections and Wall-Crossing Geometry on the Quintic del Pezzo Threefold
Abstract
Let X=V5 be the quintic del Pezzo threefold. Along the negative zero-tilt-slope paths for rational-curve ideal classes, degree five is the first degree admitting a positive point correction. We determine the resulting degree-five outer good moduli space: it is reduced with exactly two irreducible components, a normal ten-dimensional principal branch and a smooth corrected branch X×Gr(2,7). Their scheme-theoretic intersection is a normal determinantal ninefold. Along its singular locus, the principal branch has transverse rank-one 2× 4 determinantal singularities, while the intersection has the corresponding 2× 3 singularities. We construct an explicit small resolution of the principal branch as the projectivization of a rank-five extension bundle over the blow-up of the Altavilla--Petković--Rota Kuznetsov-component sixfold along its point locus. Uniform wall exclusion and point-correction bounds for degrees two through five establish the first correction threshold; the corrected degree-five factors are precisely the ideals of elliptic linear sections parametrized by Gr(2,7).
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BibTeX
@misc{fu2026point,
title = {{Point Corrections and Wall-Crossing Geometry on the Quintic del Pezzo Threefold}},
author = {Zheyuan Fu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39336},
eprint = {2610.39336},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39336},
}
RIS
TY - UNPB
TI - Point Corrections and Wall-Crossing Geometry on the Quintic del Pezzo Threefold
AU - Zheyuan Fu
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39336
UR - https://arxiv.org/abs/2610.39336
AB - Let X=V_5 be the quintic del Pezzo threefold. Along the negative zero-tilt-slope paths for rational-curve ideal classes, degree five is the first degree admitting a positive point correction. We determine the resulting degree-five outer good moduli space: it is reduced with exactly two irreducible components, a normal ten-dimensional principal branch and a smooth corrected branch X×Gr(2,7). Their scheme-theoretic intersection is a normal determinantal ninefold. Along its singular locus, the principal branch has transverse rank-one 2× 4 determinantal singularities, while the intersection has the corresponding 2× 3 singularities. We construct an explicit small resolution of the principal branch as the projectivization of a rank-five extension bundle over the blow-up of the Altavilla--Petković--Rota Kuznetsov-component sixfold along its point locus. Uniform wall exclusion and point-correction bounds for degrees two through five establish the first correction threshold; the corrected degree-five factors are precisely the ideals of elliptic linear sections parametrized by Gr(2,7).
ER -