Displaying similar documents to “Families of elliptic curves with genus 2 covers of degree 2.”

Five-gonal curves of genus nine.

Marc Coppens (2005)

Collectanea Mathematica

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Let C be a smooth 5-gonal curve of genus 9. Assume all linear systems g on C are of type I (i.e. they can be counted with multiplicity 1) and let m be the numer of linear systems g on C. The only possibilities are m=1; m=2; m=3 and m=6. Each of those possibilities occur.

The equations of space curves on a quadric.

Roberta Di Gennaro, Uwe Nagel (2007)

Collectanea Mathematica

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The homogeneous ideals of curves in a double plane have been studied by Chiarli, Greco, Nagel. Completing this work we describe the equations of any curve that is contained in some quadric. As a consequence, we classify the Hartshorne-Rao modules of such curves.

The degree of the secant variety and the join of monomial curves.

Kristian Ranestad (2006)

Collectanea Mathematica

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A monomial curve is a curve parametrized by monomials. The degree of the secant variety of a monomial curve is given in terms of the sequence of exponents of the monomials defining the curve. Likewise, the degree of the join of two monomial curves is given in terms of the two sequences of exponents.

ACM embeddings of curves of a quadric surface

S. Giuffrida, R. Maggioni, R. Re (2007)

Collectanea Mathematica

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Let C be a smooth integral projective curve admitting two pencils g and g such that g + g is birational. We give conditions in order that the complete linear system |sg + rg | be normally generated or very ample.

On the Moser-Onofri and Prékopa-Leindler inequalities.

Alessandro Ghigi (2005)

Collectanea Mathematica

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Using elementary convexity arguments involving the Legendre transformation and the Prékopa-Leindler inequality, we prove the sharp Moser-Onofri inequality, which says that 1/16π ∫|∇φ|2 + 1/4π ∫ φ - log (1/4π ∫ eφ) ≥ 0 for any funcion φ ∈ C∞(S2).

On surfaces of general type with p = q = 1, K = 3.

Francesco Polizzi (2005)

Collectanea Mathematica

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The moduli space M of surfaces of general type with p = q = 1, K = g = 3 (where g is the genus of the Albanese fibration) was constructed by Catanese and Ciliberto in [14]. In this paper we characterize the subvariety M ⊂ M corresponding to surfaces containing a genus 2 pencil, and moreover we show that there exists a non-empty, dense subset M ⊂ M which parametrizes isomorphism classes of surfaces with birational bicanonical map.

A generalization of the Nikodym boundedness theorem.

Christopher Stuart (2007)

Collectanea Mathematica

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In this note an internal property of a ring of sets, named the Nested Partition Property, is shown to imply the Nikodym Property. A wide range of examples are shown to have this property.