521 research outputs found
Explicit Resolutions of Cubic Cusp Singularities
Resolutions of cusp singularities are crucial to many techniques in computational number theory, and therefore finding explicit resolutions of these singularities has been the focus of a great deal of research. This paper presents an implementation of a sequence of algorithms leading to explicit resolutions of cusp singularities arising from totally real cubic number fields. As an example, the implementation is used to compute values of partial seta functions associated to these cusps
Non-embeddable 1-convex manifolds
We show that every small resolution of a three-dimensional terminal
hypersurface singularity can occur on a non-embeddable 1-convex manifold. We
give an explicit example of a non-embeddable manifold containing an irreducible
exceptional rational curve with normal bundle of type (1,-3). To this end we
study small resolutions of cD_4-singularities.Comment: 16 pages, 2 figures changes following referee report; some wrong
formulas correcte
New examples of modular rigid Calabi-Yau threefolds
This paper presents five new examples of modular rigid Calabi-Yau threefolds
arising from the modular elliptic surface of level 6. Explicit correspondences
to newforms of weight 4 and level 10, 17, 21, and 73 are given.Comment: 9 pages; journal-ref. added; minor mistakes correcte
A small and non-simple geometric transition
Following notation introduced in the recent paper \cite{Rdef}, this paper is
aimed to present in detail an example of a "small" geometric transition which
is not a "simple" one i.e. a deformation of a conifold transition. This is
realized by means of a detailed analysis of the Kuranishi space of a Namikawa
cuspidal fiber product, which in particular improves the conclusion of
Y.~Namikawa in Remark 2.8 and Example 1.11 of \cite{N}. The physical interest
of this example is presenting a geometric transition which can't be immediately
explained as a massive black hole condensation to a massless one, as described
by A.~Strominger \cite{Strominger95}.Comment: 22 pages. v2: final version to appear in Mathematical Physics,
Analysis and Geometry. Minor changes: title, abstract, result in Remark 3
emphasized by Theorem 5, as suggested by a referee. Some typos correcte
Explicit Solution By Radicals, Gonal Maps and Plane Models of Algebraic Curves of Genus 5 or 6
We give explicit computational algorithms to construct minimal degree (always
) ramified covers of \Prj^1 for algebraic curves of genus 5 and 6.
This completes the work of Schicho and Sevilla (who dealt with the
case) on constructing radical parametrisations of arbitrary genus curves.
Zariski showed that this is impossible for the general curve of genus .
We also construct minimal degree birational plane models and show how the
existence of degree 6 plane models for genus 6 curves is related to the
gonality and geometric type of a certain auxiliary surface.Comment: v3: full version of the pape
A singular symplectic variety of dimension 6 with a Lagrangian Prymian fibration
A projective symplectic variety of dimension 6, with only
finite quotient singularities, and
, is described as a relative compactified
Prym variety of a family of genus 4 curves with involution. It is a Lagrangian
fibration associated to a K3 surface double cover of a generic cubic surface.
It has no symplectic desingularization
Degenerations of elliptic curves and cusp singularities
We give more or less explicit equations for all two-dimensional cusp
singularities of embedding dimension at least 4. They are closely related to
Felix Klein's equations for universal curves with level n structure. The main
technical result is a description of the versal deformation of an n-gon in
. The final section contains the equations for smoothings of simple
elliptic singularities (of multiplicity at most 9).Comment: Plain Te
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