Implicitization of tensor product surfaces in the presence of a generic set of basepoints

• Type: Article in International Scientific Journal
• Date: 2017

Authors

Duarte E. (Author) Other

Journal

Title: Journal of Algebra and its Applications

Vol. 16

ISSN: 0219-4988

Publisher: World Scientific

Indexing

Scopus - 0 Citations

Other information

Authenticus ID: P-00X-9EH

DOI: 10.1142/s0219498817501894

Abstract (EN): Given a 4-dimensional vector subspace U = {f0,..,f3} of H0(P1 × P1,(a,b)), a tensor product surface, denoted by XU, is the closure of the image of the rational map ¿U: P1 × P1-¿ P3 determined by U. These surfaces arise in geometric modeling and in this context it is useful to know the implicit equation of XU in P3. In this paper, we show that if U H0(P1 × P1,(a, 1)) has a finite set of r basepoints in generic position, then the implicit equation of XU is determined by two syzygies of IU = (f0,..,f3) in bidegrees (a-r 2, 0) and (a-r 2, 0). This result is proved by understanding the geometry of the basepoints of U in P1 × P1. The proof techniques for the main theorem also apply when U is basepoint free.

Language: English

Type (Professor's evaluation): Scientific