Abstract
Given a [Formula: see text]-dimensional vector subspace [Formula: see text] of [Formula: see text], a tensor product surface, denoted by [Formula: see text], is the closure of the image of the rational map [Formula: see text] determined by [Formula: see text]. These surfaces arise in geometric modeling and in this context it is useful to know the implicit equation of [Formula: see text] in [Formula: see text]. In this paper, we show that if [Formula: see text] has a finite set of [Formula: see text] basepoints in generic position, then the implicit equation of [Formula: see text] is determined by two syzygies of [Formula: see text] in bidegrees [Formula: see text] and [Formula: see text]. This result is proved by understanding the geometry of the basepoints of [Formula: see text] in [Formula: see text]. The proof techniques for the main theorem also apply when [Formula: see text] is basepoint free.
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