Let E be a stable vector bundle of rank r and slope 2g-1\documentclass[12pt]{minimal}
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\begin{document}$$2g-1$$\end{document} on a smooth irreducible complex projective curve C of genus g≥3\documentclass[12pt]{minimal}
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\begin{document}$$g \ge 3$$\end{document}. In this paper we show a relation between theta divisor ΘE\documentclass[12pt]{minimal}
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\begin{document}$$\Theta _E$$\end{document} and the geometry of the tautological model PE\documentclass[12pt]{minimal}
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\begin{document}$$P_E$$\end{document} of E. In particular, we prove that for r>g-1\documentclass[12pt]{minimal}
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\begin{document}$$r > g-1$$\end{document}, if C is a Petri curve and E is general in its moduli space then ΘE\documentclass[12pt]{minimal}
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\begin{document}$$\Theta _E$$\end{document} defines an irreducible component of the variety parametrizing (g-2)\documentclass[12pt]{minimal}
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\begin{document}$$(g-2)$$\end{document}-linear spaces which are g-secant to the tautological model PE\documentclass[12pt]{minimal}
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\begin{document}$$P_E$$\end{document}. Conversely, for a stable, (g-2)\documentclass[12pt]{minimal}
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\begin{document}$$(g-2)$$\end{document}-very ample vector bundle E, the existence of an irreducible non special component of dimension g-1\documentclass[12pt]{minimal}
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\begin{document}$$g-1$$\end{document} of the above variety implies that E admits theta divisor.
