54 research outputs found
A high fibered power of a family of varieties of general type dominates a variety of general type
We prove the following theorem:
Fibered Power Theorem: Let X\rar B be a smooth family of positive
dimensional varieties of general type, with irreducible. Then there exists
an integer , a positive dimensional variety of general type , and a
dominant rational map X^n_B \das W_n.Comment: Latex2e (in latex 2.09 compatibility mode). To get a fun-free version
change the `FUN' variable to `n' on the second line (option dedicated to my
friend Yuri Tschinkel). Postscript file with color illustration available on
http://math.bu.edu/INDIVIDUAL/abrmovic/fibered.p
Standard monomial theory for wonderful varieties
A general setting for a standard monomial theory on a multiset is introduced
and applied to the Cox ring of a wonderful variety. This gives a degeneration
result of the Cox ring to a multicone over a partial flag variety. Further, we
deduce that the Cox ring has rational singularities.Comment: v3: 20 pages, final version to appear on Algebras and Representation
Theory. The final publication is available at Springer via
http://dx.doi.org/10.1007/s10468-015-9586-z. v2: 20 pages, examples added in
Section 3 and in Section
Sur la p-dimension des corps
Let A be an excellent integral henselian local noetherian ring, k its residue
field of characteristic p>0 and K its fraction field. Using an algebraization
technique introduced by the first named author, and the one-dimension case
already proved by Kazuya KATO, we prove the following formula: cd_p(K) = dim(A)
+ p-rank(k), if k is separably closed and K of characteristic zero. A similar
statement is valid without those assumptions on k and K
Correspondences in Arakelov geometry and applications to the case of Hecke operators on modular curves
In the context of arithmetic surfaces, Bost defined a generalized Arithmetic
Chow Group
(ACG) using the Sobolev space L^2_1. We study the behavior of these groups
under pull-back and push-forward and we prove a projection formula.
We use these results to define an action of the Hecke operators on the ACG of
modular curves and to show that they are self-adjoint with respect to the
arithmetic intersection product. The decomposition of the ACG in
eigencomponents which follows allows us to define new numerical invariants,
which are refined versions of the self-intersection of the dualizing sheaf.
Using the Gross-Zagier formula and a calculation due independently to Bost and
Kuehn we compute these invariants in terms of special values of L series. On
the other hand, we obtain a proof of the fact that Hecke correspondences acting
on the Jacobian of the modular curves are self-adjoint with respect to the
N\'eron-Tate height pairing.Comment: 38 pages. Minor correction
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