Virtual invariants of Quot schemes of points on threefolds

2025/06/17 by Solomiya Mizyuk, Mizyuk, Solomiya
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2506.14490

openalex publication_date 2025/06/17 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28

Abstract

We construct an almost perfect obstruction theory of virtual dimension zero on the Quot scheme parametrizing zero-dimensional quotients of a locally free sheaf on a smooth projective 3-fold. This gives a virtual class in degree zero and therefore allows one to define virtual invariants of the Quot scheme. We compute these invariants proving a conjecture by Ricolfi. The computation is done by reducing to the toric case via cobordism theory and a degeneration argument. The toric case is solved by reducing to the computation on the Quot scheme of points on \mathbbA³ via torus localization, the torus-equivariant Siebert's formula for almost perfect obstruction theories and the torus-equivariant Jouanolou trick.

Citations

• Derived hyperquot schemes
• The 3-fold K-theoretic DT/PT vertex correspondence holds
• The cohomology of the Quot scheme on a smooth curve as a Yangian representation
• Marked relative invariants and GW/PT correspondences
• Localizing Virtual Structure Sheaves for Almost Perfect Obstruction Theories
• The equivariant Atiyah class
• K-Theoretic Generalized Donaldson-Thomas Invariants
• Virtual classes and virtual motives of Quot schemes on threefolds
• Localizing virtual fundamental cycles for semi-perfect obstruction\n theories
• Tensor generators on schemes and stacks
• Good degeneration of Quot-schemes and coherent systems
• Deformation of quotients on a product
• Algebraic cobordism of bundles on varieties
• Virtual pull-backs
• Algebraic cobordism revisited
• The resolution property for schemes and stacks
• A Degeneration formula of GW-invariants
• Localization of virtual classes
• Virtual moduli cycles and Gromov-Witten invariants of algebraic varieties

Related

• Localizing Virtual Structure Sheaves for Almost Perfect Obstruction Theories
• Wall-crossing for punctual Quot-schemes
• Virtual classes and virtual motives of Quot schemes on threefolds
• K-Theoretic Generalized Donaldson-Thomas Invariants
• The virtual intersection theory of isotropic Quot Schemes