# A generalization of the Clifford index and determinantal equations for curves and their secant varieties - Mathematics > Algebraic Geometry

A generalization of the Clifford index and determinantal equations for curves and their secant varieties - Mathematics > Algebraic Geometry - Download this document for free, or read online. Document in PDF available to download.

Abstract: This is the author-s 2008 thesis from the University of Chicago. Wegeneralize the notion of the Clifford index to an arbitrary very ample linebundle and show how it determines when a curve and its various secant varietieshave determinantal equations. In particular we establish the scheme theoreticversion of a conjecture of Eisenbud-Koh-Stillman. If $L 1$ and $L 2$ are linebundles of degree at least $2g+1+k$, then ${ m Sec}^jC$ is determinantallypresented for $j \leq k$ and for $j \leq k+1$ if $L 1 eq L 2$. We also give ageometric characterization of the standard Clifford index in terms of whichsecant varieties of $C$ are determinantal in the bicanonical embedding. Therelationship with Koszul cohomology and Green-s conjecture is also discussed.

Author: ** Adam Ginensky**

Source: https://arxiv.org/