RT Journal Article T1 Syzygies of projective surfaces: an overview A1 Gallego Rodrigo, Francisco Javier A1 Purnaprajna, Bangere P. AB 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. PB Ramanujan Mathematical Society SN 0970-1249 YR 1999 FD 1999 LK https://hdl.handle.net/20.500.14352/58473 UL https://hdl.handle.net/20.500.14352/58473 DS Docta Complutense RD 10 abr 2025