1,721,055 research outputs found
Zeta functions of monomial deformations of delsarte hypersurfaces
Full text linkLet Xλ and X′λ be monomial deformations of two Delsarte hypersurfaces in weighted projective spaces. In this paper we give a sufficient condition so that their zeta functions have a common factor. This generalises results by Doran, Kelly, Salerno, Sperber, Voight and Whitcher [arXiv:1612.09249], where they showed this for a particular monomial deformation of a Calabi-Yau invertible polynomial. It turns out that our factor can be of higher degree than the factor found in [arXiv:1612.09249].This paper is a contribution to the Special Issue on Modular Forms and String Theory in honor of Noriko
Yui. The full collection is available at http://www.emis.de/journals/SIGMA/modular-forms.html.
The author would like to thank John Voight and Tyler Kelly for various conversations on this
topic. The author would like to thank the referees for various suggestions to improve the
exposition
The average rank of elliptic -folds
Full text linkLet be a variety of dimension at least two. We show that the density of elliptic curves with positive rank is zero if has dimension at least 3 and is at most if is a surface.Expansion of the discussion of the cycle class map; several minor change
Classification of all Jacobian elliptic fibrations on certain K3 surfaces
No full textIn this paper we classify all configurations of singular fibers of elliptic fibrations on the double cover of P-2 ramified along six lines in general position
Extremal elliptic surfaces & Infinitesimal Torelli
Full text linkWe describe in terms of the j-invariant all elliptic surfaces pi: X -> C with
a section, such that h^{1,1}(X)=rank NS(X) and the Mordell-Weil group of pi is
finite.
We use this to give a complete solution to infinitesimal Torelli for elliptic
surfaces with a section over P^1.Comment: 16 pages; 3rd version; small changes to the third and fourth sectio
Higher Noether-Lefschetz loci of elliptic surfaces
No full textWe calculate the dimension of the locus of Jacobian elliptic surfaces over P-1 with a given Picard number, in the corresponding moduli space
Nodal surfaces with obstructed deformations
Full text linkIn this text we show that the deformation space of a nodal surface of degree is smooth and of the expected dimension if or and has at most nodes. (The case was previously covered by Alexandru Dimca by using different techniques.)
For we give explicit examples of nodal surfaces with nodes, for which the tangent space to the deformation space has larger dimension than expected.
We give a short discussion on the shape of the deformation space of surfaces of the form , where is a linear form.v2: Added a reference to a similar result by Alexandru Dimca and a discussion on the difference between Dimca\u27s result and ours v3: Expanded several argument
On the classification of degree 1 elliptic threefolds with constant j-invariant
No full textWe describe the possible Mordell-Weil groups for degree 1 elliptic threefold with rational base and constant j-invariant. Moreover, we classify all such elliptic threefolds if the j-invariant is nonzero. We can use this classification to describe a class of singular hypersurfaces in P(2, 3, 1, 1, 1) that admit no variation of Hodge structure (Remark 9.3). 2013 © University of Illinois
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