Categories of massless D-branes and del Pezzo surfaces. (English) Zbl 1342.83313

Summary: 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 Kähler 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 \(\mathbb{P}^3\), the category of \(Q\)-massless objects is a “fractional Calabi-Yau” category of graded matrix factorizations.


83E30 String and superstring theories in gravitational theory
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14J81 Relationships between surfaces, higher-dimensional varieties, and physics
14J26 Rational and ruled surfaces
Full Text: DOI arXiv


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