Displaying similar documents to “Minimal resolution and stable reduction of X 0 ( N ) ”

Curves with only triple ramification

Stefan Schröer (2003)

Annales de l'Institut Fourier

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We show that the set of smooth curves of genus g ≥ 0 admitting a branched covering X → ℙ 1 with only triple ramification points is of dimension at least max ( 2 g - 3 , g ) . In characteristic two, such curves have tame rational functions and an analog of Belyi’s Theorem applies to them.

The modified diagonal cycle on the triple product of a pointed curve

Benedict H. Gross, Chad Schoen (1995)

Annales de l'institut Fourier

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Let X be a curve over a field k with a rational point e . We define a canonical cycle Δ e ∈ Z 2 ( X 3 ) hom . Suppose that k is a number field and that X has semi-stable reduction over the integers of k with fiber components non-singular. We construct a regular model of X 3 and show that the height pairing ⟨ τ * ( Δ e ) , τ * ' ( Δ e ) ⟩ is well defined where τ and τ ' are correspondences. The paper ends with a brief discussion of heights and L -functions in the case that X is a modular curve.

A condition for the rationality of certain elliptic modular forms over primes dividing the level

Andrea Mori (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let f be a weight k holomorphic automorphic form with respect to Γ 0 ⁢ N . We prove a sufficient condition for the integrality of f over primes dividing N . This condition is expressed in terms of the values at particular C ⁢ M curves of the forms obtained by iterated application of the weight k Maaß operator to f and extends previous results of the Author.

The fibre of the Prym map in genus four

Laura Hidalgo-Solís, Sevin Recillas-Pishmish (1999)

Bollettino dell'Unione Matematica Italiana

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In questa nota si dà una descrizione della fibra della mappa di Prym in genere 4. Se J ⁢ X è la Jacobiana di una curva di genere 3, allora la fibra della mappa di Prym in J ⁢ X si ottiene dalla varietà di Kummer K ⁢ X mediante due scoppiamenti: σ 1 : K ⁢ X ⁢ 0 → K ⁢ X che è lo scoppiamento di K ⁢ X nell'origine e σ 2 : K ⁢ X ⁢ 0 ~ → K ⁢ X ⁢ 0 che è lo scoppiamento lungo una curva isomorfa a X .