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Hypersurfaces in $\PP^4$ with positive defect
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Let $V$ be a hypersurface in $\PP^4$ with ordinary double and triple points as the only singularities, and let $\mu_2$ and $\mu_3$ be the number of ordinary double points (triple points, respectively) of $V$. Then we prove that if $\mu_2 +11\mu_3 \geq \frac{11d^4-50d^3+85d^2-70d+48}{24}$, then the defect of $V$ is positive.
Abstract
Let $V$ be a hypersurface in $\PP^4$ with ordinary double and triple points as the only singularities, and let $\mu_2$ and $\mu_3$ be the number of ordinary double points (triple points, respectively) of $V$. Then we prove that if $\mu_2 +11\mu_3 \geq \frac{11d^4-50d^3+85d^2-70d+48}{24}$, then the defect of $V$ is positive.
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