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On Fujita's Advanced Generalized Mukai Conjecture
Abstract
We prove Fujita's advanced generalized Mukai conjecture for smooth complex Fano varieties. Our starting point is the existence of independent two-point Gromov--Witten correspondences. We show that there are finitely many unsplit families of rational curves whose chains connect X. We use these families to bound the anticanonical degrees throughout the successive minimal horizontal construction, so every family in that construction is unsplit. Fujita's contraction theorem and inductive classification then give the required list of varieties.
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BibTeX
@misc{li2026fujitas,
title = {{On Fujita's Advanced Generalized Mukai Conjecture}},
author = {Duo Li},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05452},
eprint = {2611.05452},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05452},
}
RIS
TY - UNPB
TI - On Fujita's Advanced Generalized Mukai Conjecture
AU - Duo Li
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05452
UR - https://arxiv.org/abs/2611.05452
AB - We prove Fujita's advanced generalized Mukai conjecture for smooth complex Fano varieties. Our starting point is the existence of independent two-point Gromov--Witten correspondences. We show that there are finitely many unsplit families of rational curves whose chains connect X. We use these families to bound the anticanonical degrees throughout the successive minimal horizontal construction, so every family in that construction is unsplit. Fujita's contraction theorem and inductive classification then give the required list of varieties.
ER -