PreprintCC BY-NC-SA 4.0arXiv
Reconstruction of Fano manifolds from the orthogonal to an exceptional coherent sheaf
Abstract
Let X and Y be smooth complex Fano manifolds of dimension at least three with very ample anticanonical bundles, and let ℰX and ℰY be exceptional coherent sheaves on X and Y, respectively. We prove that a Fourier--Mukai equivalence ℰX⊥≃ ℰY⊥ implies X≃ Y.
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BibTeX
@misc{ma2026reconstruction,
title = {{Reconstruction of Fano manifolds from the orthogonal to an exceptional coherent sheaf}},
author = {Songtao Kenneth Ma},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21904},
eprint = {2610.21904},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21904},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Reconstruction of Fano manifolds from the orthogonal to an exceptional coherent sheaf
AU - Songtao Kenneth Ma
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.21904
UR - https://arxiv.org/abs/2610.21904
AB - Let X and Y be smooth complex Fano manifolds of dimension at least three with very ample anticanonical bundles, and let ℰ_X and ℰ_Y be exceptional coherent sheaves on X and Y, respectively. We prove that a Fourier--Mukai equivalence ℰ_X^⊥≃ ℰ_Y^⊥ implies X≃ Y.
ER -