Displaying similar documents to “The p -rank stratification of Artin-Schreier curves”

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 ) ) ≥ 1 and (ii) for every line ℓ on S such that ℓ ∩ C = ∅ , the normal bundle N ℓ / V is trivial (  N ℓ / V ≃ 𝒪 ℙ 1 ⊕ 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...

Finiteness results for Teichmüller curves

Martin Möller (2008)

Annales de l’institut Fourier

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We show that for each genus there are only finitely many algebraically primitive Teichmüller curves C , such that (i) C lies in the hyperelliptic locus and (ii) C is generated by an abelian differential with two zeros of order g - 1 . We prove moreover that for these Teichmüller curves the trace field of the affine group is not only totally real but cyclotomic.

The Frobenius action on rank 2 vector bundles over curves in small genus and small characteristic

Laurent Ducrohet (2009)

Annales de l’institut Fourier

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Let X be a general proper and smooth curve of genus 2 (resp. of genus 3 ) defined over an algebraically closed field of characteristic p . When 3 ≤ p ≤ 7 , the action of Frobenius on rank 2 semi-stable vector bundles with trivial determinant is completely determined by its restrictions to the 30 lines (resp. the 126 Kummer surfaces) that are invariant under the action of some order 2 line bundle over X . Those lines (resp. those Kummer surfaces) are closely related to the elliptic curves (resp....

Specializations of one-parameter families of polynomials

Farshid Hajir, Siman Wong (2006)

Annales de l’institut Fourier

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Let K be a number field, and suppose λ ( x , t ) ∈ K [ x , t ] is irreducible over K ( t ) . Using algebraic geometry and group theory, we describe conditions under which the K -exceptional set of λ , i.e. the set of α ∈ K for which the specialized polynomial λ ( x , α ) is K -reducible, is finite. We give three applications of the methods we develop. First, we show that for any fixed n ≥ 10 , all but finitely many K -specializations of the degree n generalized Laguerre polynomial L n ( t ) ( x ) are K -irreducible and have Galois group S n . Second, we study...

Galois actions on Néron models of Jacobians

Lars H. Halle (2010)

Annales de l’institut Fourier

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Let X be a smooth curve defined over the fraction field K of a complete discrete valuation ring R . We study a natural filtration of the special fiber of the Néron model of the Jacobian of X by closed, unipotent subgroup schemes. We show that the jumps in this filtration only depend on the fiber type of the special fiber of the minimal regular model with strict normal crossings for X over R , and in particular are independent of the residue characteristic. Furthermore, we obtain information...