%0 Journal Article %T What can be computed in algebraic geometry? %A Dave Bayer %A David Mumford %J Mathematics %D 1993 %I arXiv %X This paper is a survey of computational issues in algebraic geometry, with particular attention to the theory of Grobner bases and the regularity of an algebraic variety. 1. A geometric introduction to Grobner bases. 2. An algebraic introduction to Grobner bases. 3. Bounds in algebraic geometry, and regularity and complexity questions. 4. Applications. %U http://arxiv.org/abs/alg-geom/9304003v1