Clifford’s Theorem for real algebraic curves

Jean-Philippe Monnier

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Codimension $3$ Arithmetically Gorenstein Subschemes of projective $N$ -space

Robin Hartshorne, Irene Sabadini, Enrico Schlesinger (2008)

Annales de l’institut Fourier

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We study the lowest dimensional open case of the question whether every arithmetically Cohen–Macaulay subscheme of $ℙ^{N}$ is glicci, that is, whether every zero-scheme in $ℙ^{3}$ is glicci. We show that a general set of $n \geq 56$ points in $ℙ^{3}$ admits no strictly descending Gorenstein liaison or biliaison. In order to prove this theorem, we establish a number of important results about arithmetically Gorenstein zero-schemes in $ℙ^{3}$ .

Weierstrass gaps and curves on a scroll.

Carvalho, Cícero (2002)

Beiträge zur Algebra und Geometrie

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Residual representation of algebraic-geometric codes.

Hübl, Reinhold (2001)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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Quadratic Differentials and Equivariant Deformation Theory of Curves

Bernhard Köck, Aristides Kontogeorgis (2012)

Annales de l’institut Fourier

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Given a finite $p$ -group $G$ acting on a smooth projective curve $X$ over an algebraically closed field $k$ of characteristic $p$ , the dimension of the tangent space of the associated equivariant deformation functor is equal to the dimension of the space of coinvariants of $G$ acting on the space $V$ of global holomorphic quadratic differentials on $X$ . We apply known results about the Galois module structure of Riemann-Roch spaces to compute this dimension when $G$ is cyclic or when the action of $G$ on...

Computing limit linear series with infinitesimal methods

Laurent Evain (2007)

Annales de l’institut Fourier

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Alexander and Hirschowitz determined the Hilbert function of a generic union of fat points in a projective space when the number of fat points is much bigger than the greatest multiplicity of the fat points. Their method is based on a lemma which determines the limit of a linear system depending on fat points approaching a divisor. Other Hilbert functions were computed previously by Nagata. In connection with his counter-example to Hilbert’s fourteenth problem, Nagata determined...

Obstructions to deforming curves on a $3$ -fold, II: Deformations of degenerate curves on a del Pezzo $3$ -fold

Hirokazu Nasu (2010)

Annales de l’institut Fourier

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We study the Hilbert scheme ${Hilb}^{s c} V$ of smooth connected curves on a smooth del Pezzo $3$ -fold $V$ . We prove that any degenerate curve $C$ , any curve $C$ contained in a smooth hyperplane section $S$ of $V$ , does not deform to a non-degenerate curve if the following two conditions are satisfied: (i) $χ (V, ℐ_{C} (S)) \geq 1$ and (ii) for every line $ℓ$ on $S$ such that $ℓ \cap C = \emptyset$ , the normal bundle $N_{ℓ / V}$ is trivial ( $N_{ℓ / V} ≃ {𝒪_{ℙ^{1}}}^{\oplus 2}$ ). As a consequence, we prove an analogue (for ${Hilb}^{s c} V$ ) of a conjecture of J. O. Kleppe, which is concerned with non-reduced components...

Displaying similar documents to “Clifford’s Theorem for real algebraic curves”

Codimension 3 Arithmetically Gorenstein Subschemes of projective N -space

Weierstrass gaps and curves on a scroll.

Residual representation of algebraic-geometric codes.

Quadratic Differentials and Equivariant Deformation Theory of Curves

Computing limit linear series with infinitesimal methods

Obstructions to deforming curves on a 3 -fold, II: Deformations of degenerate curves on a del Pezzo 3 -fold

Codimension $3$ Arithmetically Gorenstein Subschemes of projective $N$ -space

Obstructions to deforming curves on a $3$ -fold, II: Deformations of degenerate curves on a del Pezzo $3$ -fold