Derived autoequivalences and a weighted Beilinson resolution

Canonaco, Alberto; Karp, R. L.

doi:10.1016/j.geomphys.2008.01.004

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Given a smooth stacky Calabi-Yau hypersurface X in a weighted projective space, we consider the functor G which is the composition of the following two autoequivalences of D^b(X): the first one is induced by the spherical object O_X, while the second one is tensoring with O_X(1). The main result of the paper is that the composition of G with itself w times, where w is the sum of the weights of the weighted projective space, is isomorphic to the autoequivalence "shift by 2". The proof also involves the construction of a Beilinson type resolution of the diagonal for weighted projective spaces, viewed as smooth stacks.

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Titolo:	Derived autoequivalences and a weighted Beilinson resolution
Autori:	CANONACO, ALBERTO R. L. KARP mostra contributor esterni nascondi contributor esterni
Data di pubblicazione:	2008
Rivista:	JOURNAL OF GEOMETRY AND PHYSICS
Abstract:	Given a smooth stacky Calabi-Yau hypersurface X in a weighted projective space, we consider the functor G which is the composition of the following two autoequivalences of D^b(X): the first one is induced by the spherical object O_X, while the second one is tensoring with O_X(1). The main result of the paper is that the composition of G with itself w times, where w is the sum of the weights of the weighted projective space, is isomorphic to the autoequivalence "shift by 2". The proof also involves the construction of a Beilinson type resolution of the diagonal for weighted projective spaces, viewed as smooth stacks.
Handle:	http://hdl.handle.net/11571/102700
Appare nelle tipologie:	1.1 Articolo in rivista

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