Title: Triangulated Categories of Matrix Factorizations for Elliptic Singularities 

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AbstractF
We study the triangulated category of graded matrix factorizations for a simply elliptic singularity, which has the Gorenstein parameter ƒĆ = 0. The singularity admits a natural C~-action so that the quotient is an elliptic curve. From a view point of mirror symmetry, it is natural to consider finite group extensions of the action so that the quotients are P1-orbifolds. Then, the triangulated category of matrix factorizations equivariant with those group actions admit a Serre functor.
In the present paper, we explicitly determine the matrix factorizations, which give the full strongly exceptional collections of the categories, which form elliptic Dynkin quivers associated with elliptic root systems. Therefore, the category is equivalent to the derived category of the representations of the elliptic Dynkin quiver.

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<a href="http://www.math.s.chiba-u.ac.jp/~kajiura/mirror2012/oda.pdf"> [Abstract of his master thesis]</a>