Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homaloidal hypersurfaces and hypersurfaces with vanishing Hessian   We prove the existence of various families of irreducible homaloidal
hypersurfaces in projective space $\mathbb P^ r$, for all $r\geq 3$. Some of
these are families of homaloidal hypersurfaces whose degrees are arbitrarily
large as compared to the dimension of the ambient projective space. The
existence of such a family solves a question that has naturally arisen from the
consideration of the classes of homaloidal hypersurfaces known so far. The
result relies on a fine analysis of dual hypersurfaces to certain scroll
surfaces. We also introduce an infinite family of determinantal homaloidal
hypersurfaces based on a certain degeneration of a generic Hankel matrix. These
examples fit non--classical versions of de Jonqui\`eres transformations. As a
natural counterpoint, we broaden up aspects of the theory of Gordan--Noether
hypersurfaces with vanishing Hessian determinant, bringing over some more
precision to the present knowledge.

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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: stat