Categories of Massless D-Branes and del Pezzo Surfaces

Abstract

In analogy with the physical concept of a massless D-brane, we define a notion of "Q-masslessness" for objects in the derived category. This is defined in terms of monodromy around singularities in the stringy Kahler moduli space and is relatively easy to study using spherical functors. We consider several examples in which del Pezzo surfaces and other rational surfaces in Calabi-Yau threefolds are contracted. For precisely the del Pezzo surfaces that can be written as hypersurfaces in weighted P3, the category of Q-massless objects is a "fractional Calabi-Yau" category of graded matrix factorizations.

LaTeX, 40 pages, refs added

References in corpus (5)

• Phases Of N=2 Theories In 1+1 Dimensions With Boundary
• New derived symmetries of some hyperkähler varieties
• Derived categories of cubic and V14 threefolds
• D-Branes on Toric Calabi-Yau Varieties
• Probing Geometry with Stability Conditions

Cited by in corpus (10)

• P-functor versions of the Nakajima operators
• Perverse sheaves of categories and some applications
• On genus-0 invariants of Calabi-Yau hybrid models
• Spherical functors on the Kummer surface
• Universal functors on symmetric quotient stacks of Abelian varieties
• Mirror Symmetry and Discriminants
• Noncommutative resolutions and CICY quotients from a non-abelian GLSM
• General Mirror Pairs for Gauged Linear Sigma Models
• Exoflops in Two Dimensions
• On the derived category of the Hilbert scheme of points on an Enriques surface