3,726 research outputs found
On the Newton polygons of abelian varieties of Mumford's type
Let be an abelian variety of Mumford's type. This paper determines all
possible Newton polygons of in char . This work generalizes a result of
R. Noot.Comment: 15 page
Complex multiplication, Griffiths-Yukawa couplings, and rigidity for families of hypersurfaces
Let M(d,n) be the moduli stack of hypersurfaces of degree d > n in the
complex projective n-space, and let M(d,n;1) be the sub-stack, parameterizing
hypersurfaces obtained as a d fold cyclic covering of the projective n-1 space,
ramified over a hypersurface of degree d. Iterating this construction, one
obtains M(d,n;r).
We show that M(d,n;1) is rigid in M(d,n), although the Griffiths-Yukawa
coupling degenerates for dn the sub-stack
M(d,n;2) deforms.
We calculate the exact length of the Griffiths-Yukawa coupling over M(d,n;r),
and we construct a 4-dimensional family of quintic hypersurfaces, and a dense
set of points in the base, where the fibres have complex multiplication.Comment: 38 pages, amsLaTeX, second version: Correction of a wrong statment in
Section 8; References updated, some typos corrected (including one in the
title
On the slope conjecture of Barja and Stoppino for fibred surfaces
Let be a locally non-trivial relatively minimal fibration of
genus with relative irregularity . It was conjectured by Barja
and Stoppino that the slope . We prove the
conjecture when is small with respect to ; we also construct
counterexamples when is odd and .Comment: any comment is welcom
A characterization of certain Shimura curves in the moduli stack of abelian varieties
Let f:X-->Y be a semi-stable family of complex abelian varieties over a curve
Y of genus q, and smooth over the complement of s points. If F(1,0) denotes the
non-flat (1,0) part of the corresponding variation of Hodge structures, the
Arakelov inequalities say that 2deg(F(1,0)) is bounded from above by
g=rank(F(1,0))(2q-2+s).
We show that for s>0 families reaching this bound are isogenous to the g-fold
product of a modular family of elliptic curves, and a constant abelian variety.
For s=0, if the flat part of the VHS is defined over the rational numbers,
the family is isogeneous to the g-fold product of a family h:Z-->Y, and a
constant abelian variety. In this case, h:Z-->Y is obtained from the
corestriction of a quaternion algebra A, defined over a totally real
numberfield F, and ramified over all infinite places but one.
In case the flat part of the VHS is not defined over the rational numbers, we
determine the structure of the VHS.Comment: 42 pages, AMSLaTeX, Added one proposition, one remark, and erased one
chapter with examples. References update
Weierstrass filtration on Teichmuller curves and Lyapunov exponents
We define the Weierstrass filtration for Teichmuller curves and construct the
Harder-Narasimhan filtration of the Hodge bundle of a Teichmuller curve in
hyperelliptic loci and low-genus nonvarying strata. As a result we obtain the
sum of Lyapunov exponents of Teichmuller curves in these strata.Comment: 28 pages. Published version in Journal of Modern Dynamics. arXiv
admin note: text overlap with arXiv:1104.3932 by other author
Complex projective threefolds with non-negative canonical Euler-Poincare characteristic
Let be a complex nonsingular projective 3-fold of general type with
(resp. ). We prove that the m-canonical map
is birational onto its image for all (resp. ). Known examples show that the lower bound (resp. ) is optimal.Comment: 20 pages, to appear in "Communications in Analysis and Geometry
Weierstrass filtration on Teichm\"uller curves and Lyapunov exponents: Upper bounds
We get an upper bound of the slope of each graded quotient for the
Harder-Narasimhan filtration of the Hodge bundle of a Teichm\"{u}ller curve. As
an application, we show that the sum of Lyapunov exponents of a Teichm\"{u}ller
curve does not exceed , with equality reached if and only if the
curve lies in the hyperelliptic locus induced from
or it is a special Teichm\"{u}ller curve
in . It also gives an unified interpretation for
many known results about the special partial sums of Lyapunov exponents on
Teichm\"uller curves.Comment: 19 page. We rewrite this paper without changing the mathematics
conten
On Shimura curves in the Torelli locus of curves
Oort has conjectured that there do not exist Shimura curves lying generically
in the Torelli locus of curves of genus . We show that there do not
exist one-dimensional Shimura families of semi-stable curves of genus
of Mumford type. We also show that there do not exist Shimura curves lying
generically in the Torelli locus of hyperelliptic curves of genus .
The first result proves a slightly weaker form of the conjecture for the case
of Shimura curves of Mumford type. The second result proves the conjecture for
the Torelli locus of hyperelliptic curves. We also present examples of Shimura
curves contained generically in the Torelli locus of curves of genus and
.Comment: 42 pages. Some typos are corrected. comments are welcom
Discreteness of minimal models of Kodaira dimension zero and subvarieties of moduli stacks
We extend some of the results obtained for subvarieties of the moduli stack
of canonically polarized manifolds in "Base spaces of non-isotrivial families
of smooth minimal models" (math.AG/0103122) to moduli of polarized minimal
models of Kodaira dimension zero. To this aim we first show that for those
manifolds there are no non isotrivial families of minimal models, which are
birationally isotrivial. In the last chapter, we discuss the rigidity of curves
in the moduli stack of canonically polarized manifolds and of polarized minimal
models of Kodaira dimension zero.Comment: 26 pages, AMSLaTeX, 3nd version with some minor corrections and a new
introductio
Families of abelian varieties over curves with maximal Higgs field
Let f:X-->Y be a semi-stable family of complex abelian varieties over a curve
Y of genus q, and smooth over the complement of s points. If F(1,0) denotes the
non-flat (1,0) part of the corresponding variation of Hodge structures, the
Arakelov inequalities say that 2deg(F(1,0)) is bounded from above by
g=rank(F(1,0))(2q-2+s).
We show that for s>0 families reaching this bound are isogenous to the g-fold
product of a modular family of elliptic curves, and a constant abelian variety.
The content of this note became part of the article "A characterization of
certain Shimura curves in the moduly stack of abelian varieties"
(math.AG/0207228), where we also handle the case s=0.Comment: 13 pages, Latex, two minor errors corrected, the content of this note
became part of math.AG/020722
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