Gallego Rodrigo, Francisco JavierPurnaprajna, Bangere P.2023-06-202023-06-2019990970-1249https://hdl.handle.net/20.500.14352/58473This 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.journal articlehttp://www.ramanujanmathsociety.org/publications/journal-of-the-rmshttp://www.ramanujanmathsociety.org/homemetadata only access512.7Surfaces with positive irregularityKoszul cohomology groupsPositive Kodaira dimensionGeometria algebraica1201.01 Geometría Algebraica