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Explicit Rationality of Some Special Fano Fourfolds
Recent results of Hassett, Kuznetsov and others pointed out countably many divisors $$...
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Postulation of generic lines and one double line in \(\mathbb {P}^n\) in view of generic lines and one multiple linear space
A well-known theorem by Hartshorne and Hirschowitz (in: Aroca, Buchweitz, Giusti, Merle (eds) Algebraic geometry. Lecture notes in mathematics,...
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All cubics are self-isotomic
We prove that all cubics are self-isotomic.
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Algebraic boundaries of convex semi-algebraic sets
We study the algebraic boundary of a convex semi-algebraic set via duality in convex and algebraic geometry. We generalise the correspondence of...
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Generalized varieties of sums of powers
Let X ⊂ P N be an irreducible, non-degenerate variety. The generalized variety of sums of powers V S P H X ( h ) of X is the closure in the Hilbert...
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On the tangentially degenerate curves, II
A projective curve X in ℙ N is said to be tangentially degenerate if a tangent line to X at a general point P meets X again at a point other than P ....
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Linear subspaces of symmetric tensors whose non-zero elements have at least a prescribed rank
We introduce large vector spaces M of multivariate homogeneous polynomials with a prescribed lower bound for the rank of each non-zero element of M .
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Ordinary Curves, Webs and the Ubiquity of the Weak Lefschetz Property
In this short note we establish a close relationship between two a priori unrelated problems: (1) the existence of ordinary curves in ℙ ...
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Symmetric tensor rank over an infinite field
Here we prove two upper bounds (one for bivariate polynomials, one for multivariate ones) for the symmetric tensor rank with respect to an infinite...
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All cubics are self-isogonal
We develop techniques to prove that a cubic curve is invariant under the isogonal transformation of the projective plane determined by some triangle.
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Generalized Hamming weights of codes obtained from smooth plane curves
Here we study the small weight codewords and the generalized Hamming weights of Goppa codes on a smooth plane curve C in terms of the intersection of C ...