Equivariant Derived Categories Associated to a Sum of Potentials
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Date
2017-09-06
Authors
Lim, Bronson
Journal Title
Journal ISSN
Volume Title
Publisher
University of Oregon
Abstract
We construct a semi-orthogonal decomposition for the equivariant derived category of a hypersurface associated to the sum of two potentials. More specifically, if $f,g$ are two homogeneous poynomials of degree $d$ defining smooth Calabi-Yau or general type hypersurfaces in $\mathbb{P}^n$, we construct a semi-orthogonal decomposition of $D[V(f\oplus g)/\mu_d]$. Moreover, every component of the semi-orthogonal decomposition is explicitly given by Fourier-Mukai functors.
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Keywords
Algebraic geometry, Derived categories