Derived categories of curves as components of Fano manifolds

Abstract

We prove that the derived category $D(C)$ of a generic curve of genus greater than one embeds into the derived category $D(M)$ of the moduli space $M$ of rank two stable bundles on $C$ with fixed determinant of odd degree.

arXiv comment20 pages; v2: exposition improved, some references added

References in corpus (3)

• Semiorthogonal decomposition for algebraic varieties
• Exceptional collections for Grassmannians of isotropic lines
• Hyperplane sections and derived categories

Cited by in corpus (16)

• Hilbert schemes of lines and conics and automorphism groups of Fano threefolds
• Derived categories of (nested) Hilbert schemes
• Motivic decompositions of moduli spaces of vector bundles on curves
• Derived categories of flips and cubic hypersurfaces
• Categorical absorptions of singularities and degenerations
• Decompositions of moduli spaces of vector bundles and graph potentials
• Embedding derived categories of Enriques surfaces into derived categories of Fano varieties
• Retour sur l'arithmétique des intersections de deux quadriques, avec un appendice par A. Kuznestov
• Fano visitors, Fano dimension and orbifold Fano hosts
• Semiorthogonal decomposition of ${\mathrm{D}}^b({\mathrm{Bun}}_2^L)$
• Partial semiorthogonal decompositions for quiver moduli
• Vector fields and admissible embeddings for quiver moduli
• Derived category of moduli of parabolic bundles on ${\mathbb{P}}^1$
• Construction of noncommutative surfaces with exceptional collections of length 4
• Smooth components on special iterated Hilbert schemes
• Positivity of the Poincaré bundle on the moduli space of vector bundles and its applications