The authors define divisible weighted projective spaces, give sharp bounds for minimal-degree non-degenerate subvarieties therein, and develop a theory of weighted determinantal scrolls that achieve minimal degree while satisfying weighted N_p properties tied to regularity notions.
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Under a codimension assumption on the singular locus, isomorphism of the m-th differential sheaf implies isomorphisms for all lower i on complex hypersurfaces, with a positive characteristic analogue discussed.
Establishes geodesic connectedness from completeness for affine connections on statistical manifolds with divisible cubic forms, producing a Cartan-Hadamard theorem.
No complete non-orientable minimal surfaces of finite total curvature in R^3 with one end foliated by closed curvature lines exist.
citing papers explorer
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Varieties of minimal degree in weighted projective space
The authors define divisible weighted projective spaces, give sharp bounds for minimal-degree non-degenerate subvarieties therein, and develop a theory of weighted determinantal scrolls that achieve minimal degree while satisfying weighted N_p properties tied to regularity notions.
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Higher singularities for hypersurfaces
Under a codimension assumption on the singular locus, isomorphism of the m-th differential sheaf implies isomorphisms for all lower i on complex hypersurfaces, with a positive characteristic analogue discussed.
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Geodesic Connectedness on Statistical Manifolds with Divisible Cubic Forms
Establishes geodesic connectedness from completeness for affine connections on statistical manifolds with divisible cubic forms, producing a Cartan-Hadamard theorem.
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Minimal surfaces with closed curvature lines
No complete non-orientable minimal surfaces of finite total curvature in R^3 with one end foliated by closed curvature lines exist.
- K-theory of Gieseker variety and type A cyclotomic Hecke algebra