Virtual classes and virtual motives of Quot schemes on threefolds

2019/06/06 by Ricolfi, Andrea T. · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1906.02557

Abstract

For a simple, rigid vector bundle F on a Calabi-Yau 3-fold Y, we construct a symmetric obstruction theory on the Quot scheme \textrmQuot_Y(F,n), and we solve the associated enumerative theory. We discuss the case of other 3-folds. Exploiting the critical structure on \textrmQuot_{\mathbb A³}(\mathscr O^r,n), we construct a virtual motive (in the sense of Behrend-Bryan-Szendrői) for \textrmQuot_Y(F,n) for an arbitrary vector bundle F on a smooth 3-fold Y. We compute the associated motivic partition function. We obtain new examples of higher rank (motivic) Donaldson-Thomas invariants.

Cited by

• Virtual invariants of Quot schemes of points on threefolds

Related

• Motivic degree zero Donaldson-Thomas invariants
• Virtual pullbacks in Donaldson-Thomas theory of Calabi-Yau 4-folds
• Virtual invariants of Quot schemes of points on threefolds
• Higher rank motivic Donaldson-Thomas invariants of \mathbbA³ via wall-crossing, and asymptotics
• Low degree motivic Donaldson-Thomas invariants of the three-dimensional projective space