818 research outputs found
Dynamics of Special Points on Intermediate Jacobians
We prove some general density statements about the subgroup of invertible
points on intermediate jacobians; namely those points in the Abel-Jacobi image
of nullhomologous algebraic cycles on projective algebraic manifolds.Comment: 10 page
Introduction to Arithmetic Mirror Symmetry
We describe how to find period integrals and Picard-Fuchs differential
equations for certain one-parameter families of Calabi-Yau manifolds. These
families can be seen as varieties over a finite field, in which case we show in
an explicit example that the number of points of a generic element can be given
in terms of p-adic period integrals. We also discuss several approaches to
finding zeta functions of mirror manifolds and their factorizations. These
notes are based on lectures given at the Fields Institute during the thematic
program on Calabi-Yau Varieties: Arithmetic, Geometry, and Physics
Pure Spinor Integration from the Collating Formula
We use the technique developed by Becchi and Imbimbo to construct a
well-defined BRST-invariant path integral formulation of pure spinor
amplitudes. The space of pure spinors can be viewed from the algebraic geometry
point of view as a collection of open sets where the constraints can be solved
and a free independent set of variables can be defined. On the intersections of
those open sets, the functional measure jumps and one has to add boundary terms
to construct a well-defined path integral. The result is the definition of the
pure spinor integration measure constructed in term of differential forms on
each single patch.Comment: 22 page
Arithmetically Cohen-Macaulay Bundles on complete intersection varieties of sufficiently high multidegree
Recently it has been proved that any arithmetically Cohen-Macaulay (ACM)
bundle of rank two on a general, smooth hypersurface of degree at least three
and dimension at least four is a sum of line bundles. When the dimension of the
hypersurface is three, a similar result is true provided the degree of the
hypersurface is at least six. We extend these results to complete intersection
subvarieties by proving that any ACM bundle of rank two on a general, smooth
complete intersection subvariety of sufficiently high multi-degree and
dimension at least four splits. We also obtain partial results in the case of
threefolds.Comment: 15 page
--geometry of the Toda systems associated with non-exceptional simple Lie algebras
The present paper describes the --geometry of the Abelian finite
non-periodic (conformal) Toda systems associated with the and series
of the simple Lie algebras endowed with the canonical gradation. The principal
tool here is a generalization of the classical Pl\"ucker embedding of the
-case to the flag manifolds associated with the fundamental representations
of , and , and a direct proof that the corresponding K\"ahler
potentials satisfy the system of two--dimensional finite non-periodic
(conformal) Toda equations. It is shown that the --geometry of the type
mentioned above coincide with the differential geometry of special holomorphic
(W) surfaces in target spaces which are submanifolds (quadrics) of with
appropriate choices of . In addition, these W-surfaces are defined to
satisfy quadratic holomorphic differential conditions that ensure consistency
of the generalized Pl\"ucker embedding. These conditions are automatically
fulfiled when Toda equations hold.Comment: 30 pages, no figur
Period- and mirror-maps for the quartic K3
We study in detail mirror symmetry for the quartic K3 surface in P3 and the
mirror family obtained by the orbifold construction. As explained by Aspinwall
and Morrison, mirror symmetry for K3 surfaces can be entirely described in
terms of Hodge structures. (1) We give an explicit computation of the Hodge
structures and period maps for these families of K3 surfaces. (2) We identify a
mirror map, i.e. an isomorphism between the complex and symplectic deformation
parameters, and explicit isomorphisms between the Hodge structures at these
points. (3) We show compatibility of our mirror map with the one defined by
Morrison near the point of maximal unipotent monodromy. Our results rely on
earlier work by Narumiyah-Shiga, Dolgachev and Nagura-Sugiyama.Comment: 29 pages, 3 figure
Does relatedness influence migratory timing and behaviour in Atlantic salmon smolts?
Aggregating and moving with relatives may enable animals to increase opportunities for kin selection to occur. To gain group-living benefits, animals must coordinate their behaviour. Atlantic salmon, Salmo salar, demonstrate both territoriality and schooling: the two key social behaviours performed by fish. In this investigation we compared the migratory timing and behaviour of six distinct full-sibling groups of tagged S. salar smolts with a large control sample from the same wild population. The results clearly demonstrate that the incidence of schooling and diel migratory timing is not significantly influenced by relatedness, and this adds further support to the hypothesis that S. salar smolt migration is primarily an adaptive response to environmental conditions, rather than a behaviour based solely on genetics or kin-biased behaviour. Used in conjunction with the results of two previous investigations, this is the first study to illustrate that kin discrimination among full-sibling groups of parr does not lead to kin-biased schooling in smolts. Thus, even within the same full-sibling groups, the extent of kin-biased behaviour in fish can both differ within a life history stage under varying ecological conditions and shift from one life history stage to the next
Families of Quintic Calabi-Yau 3-Folds with Discrete Symmetries
At special loci in their moduli spaces, Calabi-Yau manifolds are endowed with
discrete symmetries. Over the years, such spaces have been intensely studied
and have found a variety of important applications. As string compactifications
they are phenomenologically favored, and considerably simplify many important
calculations. Mathematically, they provided the framework for the first
construction of mirror manifolds, and the resulting rational curve counts.
Thus, it is of significant interest to investigate such manifolds further. In
this paper, we consider several unexplored loci within familiar families of
Calabi-Yau hypersurfaces that have large but unexpected discrete symmetry
groups. By deriving, correcting, and generalizing a technique similar to that
of Candelas, de la Ossa and Rodriguez-Villegas, we find a calculationally
tractable means of finding the Picard-Fuchs equations satisfied by the periods
of all 3-forms in these families. To provide a modest point of comparison, we
then briefly investigate the relation between the size of the symmetry group
along these loci and the number of nonzero Yukawa couplings. We include an
introductory exposition of the mathematics involved, intended to be accessible
to physicists, in order to make the discussion self-contained.Comment: 54 pages, 3 figure
Transition-metal-free amine oxidation : a chemoselective strategy for the late-stage formation of lactams
A metal-free strategy for the formation of lactams via selective oxidation of cyclic secondary and tertiary amines is described. Molecular iodine facilitates both chemoselective and regioselective oxidation of C–H bonds directly adjacent to a cyclic amine. The mild conditions, functional group tolerance, and substrate scope are demonstrated using a suite of diverse small molecule cyclic amines, including clinically approved drug scaffolds
Invariant Homology on Standard Model Manifolds
Torus-fibered Calabi-Yau threefolds Z, with base dP_9 and fundamental group
pi_1(Z)=Z_2 X Z_2, are reviewed. It is shown that Z=X/(Z_2 X Z_2), where X=B
X_{P_1} B' are elliptically fibered Calabi-Yau threefolds that admit a freely
acting Z_2 X Z_2 automorphism group. B and B' are rational elliptic surfaces,
each with a Z_2 X Z_2 group of automorphisms. It is shown that the Z_2 X Z_2
invariant classes of curves of each surface have four generators which produce,
via the fiber product, seven Z_2 X Z_2 invariant generators in H_4(X,Z). All
invariant homology classes are computed explicitly. These descend to produce a
rank seven homology group H_4(Z,Z) on Z. The existence of these homology
classes on Z is essential to the construction of anomaly free, three family
standard-like models with suppressed nucleon decay in both weakly and strongly
coupled heterotic superstring theory.Comment: 57 pages, 13 figure
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