## LINEAR DETERMINANTAL EQUATIONS FOR ALL PROJECTIVE SCHEMES (2009)

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by
Jessica Sidman
,
Gregory G. Smith

Citations: | 1 - 0 self |

### BibTeX

@MISC{Sidman09lineardeterminantal,

author = {Jessica Sidman and Gregory G. Smith},

title = {LINEAR DETERMINANTAL EQUATIONS FOR ALL PROJECTIVE SCHEMES},

year = {2009}

}

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### Abstract

We prove that every projective embedding of a connected scheme determined by the complete linear series of a sufficiently ample line bundle is defined by the 2×2 minors of a 1-generic matrix of linear forms. Extending the work of Eisenbud-Koh-Stillman for integral curves, we also provide effective descriptions for such determinantally presented ample line bundles on products of projective spaces, Gorenstein toric varieties, and smooth n-folds.