Tensor product surfaces and linear syzygies

• Type: Article in International Scientific Journal
• Date: 2016

Authors

Duarte E. (Author) Other; Schenck H. (Author) Other

Journal

Title: Proceedings of the American Mathematical Society

Vol. 144

Pages: 65-72

ISSN: 0002-9939

Publisher: American Mathematical Society

Indexing

Scopus - 4 Citations

Other information

Authenticus ID: P-00X-9EG

DOI: 10.1090/proc/12703

Abstract (EN): Let U ¿ H0(O¿1׿1 (a, b)) be a basepoint free four-dimensional vector space, with a, b ¿ 2. The sections corresponding to U determine a regular map ¿U : ¿1 × ¿1 ¿ ¿3. We show that there can be at most one linear syzygy on the associated bigraded ideal IU ¿ k[s, t; u, v]. Existence of a linear syzygy, coupled with the assumption that U is basepoint free, implies the existence of an additional ¿special pair¿ of minimal first syzygies. Using results of Botbol, we show that these three syzygies are sufficient to determine the implicit equation of ¿U (¿1 × ¿1), and that Sing(¿U (¿1 × ¿1)) contains a line.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 7