Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Derived categories of singular surfaces   We develop an approach that allows to construct semiorthogonal decompositions
of derived categories of surfaces with cyclic quotient singularities whose
components are equivalent to derived categories of local finite dimensional
algebras. We first explain how to induce a semiorthogonal decomposition of a
surface $X$ with rational singularities from a semiorthogonal decomposition of
its resolution. In the case when $X$ has cyclic quotient singularities, we
introduce the condition of adherence for the components of the semiorthogonal
decomposition of the resolution that allows to identify the components of the
induced decomposition with derived categories of local finite dimensional
algebras. Further, we present an obstruction in the Brauer group of $X$ to the
existence of such semiorthogonal decomposition, and show that in the presence
of the obstruction a suitable modification of the adherence condition gives a
semiorthogonal decomposition of the twisted derived category of $X$. We
illustrate the theory by exhibiting a semiorthogonal decomposition for the
untwisted or twisted derived category of any normal projective toric surface
depending on whether its Weil divisor class group is torsion-free or not. For
weighted projective planes we compute the generators of the components
explicitly and relate our results to the results of Kawamata based on iterated
extensions of reflexive sheaves of rank 1.

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The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs