Communications in Analysis and Geometry

Volume 23 (2015)

Number 4

Good degeneration of Quot-schemes and coherent systems

Pages: 841 – 921



Jun Li (Department of Mathematics, Stanford University, Stanford, California, U.S.A.)

Baosen Wu (Department of Mathematics, Harvard University, Cambridge, Massachusetts, U.S.A.)


We construct good degenerations of Quot-schemes and coherent systems using the stack of expanded degenerations. We show that these good degenerations are separated and proper DM stacks of finite type. Applying to the projective threefolds, we derive degeneration formulas for DT-invariants of ideal sheaves and PT stable pair invariants.

Published 13 August 2015