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Syzygies of projective surfaces: an overview

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1999

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Ramanujan Mathematical Society
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This is a survey article concerning the syzygies of projective smooth varieties, with particular emphasis on the surface case. It describes some special cases of surfaces in which the so-called Mukai conjecture holds (namely, if KX is the canonical bundle and A is an ample line bundle then the conjecture says that KX+mA satisfies the Np-property for m≥p+4). In higher dimension the case of Calabi-Yau threefolds and the example of the Veronese embedding of Pn are considered.

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