Naga Venkata
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 Jul 2 awarded Curious Apr 25 comment On infinitesimal neighbourhood of a point in a projective scheme @Achinger: Thanks for the answer. Apr 25 accepted On infinitesimal neighbourhood of a point in a projective scheme Apr 24 revised On infinitesimal neighbourhood of a point in a projective scheme deleted 1 character in body Apr 24 revised On infinitesimal neighbourhood of a point in a projective scheme edited title Apr 24 revised On infinitesimal neighbourhood of a point in a projective scheme edited title Apr 24 asked On infinitesimal neighbourhood of a point in a projective scheme Dec 2 revised Global sections of the structure sheaf of a non-reduced projective scheme added 146 characters in body Dec 2 revised Global sections of the structure sheaf of a non-reduced projective scheme edited title Dec 2 revised Global sections of the structure sheaf of a non-reduced projective scheme edited title Dec 2 comment Global sections of the structure sheaf of a non-reduced projective scheme No. The ideal of $2l+C'$ does not contain the ideal of the plane. See "Le Schema de Hilbert des Courbes gauches localement Cohen-Macualay n'est (presque) jamais reduit" by M Martin-Descamps and D. Perrin Proposition $0.6$ for such examples. Dec 2 comment Global sections of the structure sheaf of a non-reduced projective scheme Why the down vote? Is it a trivial question or is there something very unclear? Dec 2 comment Global sections of the structure sheaf of a non-reduced projective scheme $C$ is not necessarily a plane curve. I do not know how else to write it. I meant that the curve is the scheme associated to an effective divisor on a surface. Using the adjunction formula one sees that the arithmetic genus depends on the degree of the surface. For example take a smooth surface containing $l, C'$. This will also contain the curve $2l+C'$ as a Weil divisor. But the genus depends on the degree of the surface. Dec 2 revised Global sections of the structure sheaf of a non-reduced projective scheme edited tags Dec 2 asked Global sections of the structure sheaf of a non-reduced projective scheme Nov 29 comment Hypersurfaces with Picard group generated by classes of lines on the same plane @Huizenga: The motivation comes from the study of Noether-Lefschetz locus which I unfortunately do not think is possible to explain in a paragraph. I am sorry. I would expect that for $d$ large enough this phenomenon happens. Again this is motivated by results on Noether-Lefschetz locus. Nov 29 comment Hypersurfaces with Picard group generated by classes of lines on the same plane @Bright: The base field in $\mathbb{C}$. Nov 28 asked Hypersurfaces with Picard group generated by classes of lines on the same plane Nov 23 revised Deformation of a family of curves in a surface added 39 characters in body Nov 23 comment Deformation of a family of curves in a surface @Huizenga: Sorry, I meant open subset of $B$.