Develops an infinitesimal quotient criterion via the Milnor algebra for generic finiteness of hyperplane-section maps on hypersurfaces with isolated singularities, recovering Lefschetz in the smooth case and applying to curves and surfaces.
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Optimal L^p-L^q boundedness regions are derived for local maximal operators on homogeneous polynomial hypersurfaces in R^3, depending on height and level-set curve type, plus global estimates without transversality.
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Jacobian algebras and variation of hyperplane sections
Develops an infinitesimal quotient criterion via the Milnor algebra for generic finiteness of hyperplane-section maps on hypersurfaces with isolated singularities, recovering Lefschetz in the smooth case and applying to curves and surfaces.
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Maximal functions related to homogeneous hypersurfaces in $\mathbb{R}^3$
Optimal L^p-L^q boundedness regions are derived for local maximal operators on homogeneous polynomial hypersurfaces in R^3, depending on height and level-set curve type, plus global estimates without transversality.