2025/11/26 by Xu, Chunkai
#14F06 #14F08 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2511.21288
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.