Stronger Bogomolov--Gieseker type inequality on quintic threefold

Chunkai Xu

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arXiv · 2511.21288

Stronger Bogomolov--Gieseker type inequality on quintic threefold

Chunkai Xu

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Abstract

We establish a stronger Bogomolov--Gieseker type inequality for slope-semistable sheaves on the smooth quintic threefold. Our approach combines a refined restriction theorem for tilt-stable objects with explicit Clifford-type bounds for semistable bundles on plane quintic curves. As a consequence, we obtain an explicit piecewise linear inequality on the Chern characters of any slope-semistable sheaf improving upon the classical Bogomolov--Gieseker bound and implying Toda's conjectural inequality. The method also yields a stronger Bogomolov--Gieseker type inequality on smooth quintic surfaces. These results provide new evidence toward the existence of a Bridgeland stability condition of Gepner type on the quintic threefold.

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BibTeX RIS

Chunkai Xu. 2025-11-26. Stronger Bogomolov--Gieseker type inequality on quintic threefold. https://arxiv.org/abs/2511.21288

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