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# Some Results on Surfaces of General Type

Published:2005-08-01
Printed: Aug 2005
• B. P. Purnaprajna
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## Abstract

In this article we prove some new results on projective normality, normal presentation and higher syzygies for surfaces of general type, not necessarily smooth, embedded by adjoint linear series. Some of the corollaries of more general results include: results on property $N_p$ associated to $K_S \otimes B^{\otimes n}$ where $B$ is base-point free and ample divisor with $B\otimes K^*$ {\it nef}, results for pluricanonical linear systems and results giving effective bounds for adjoint linear series associated to ample bundles. Examples in the last section show that the results are optimal.
 MSC Classifications: 13D02 - Syzygies, resolutions, complexes 14C20 - Divisors, linear systems, invertible sheaves 14J29 - Surfaces of general type