In this paper we recall the construction and basic properties of complex Shimura varieties and show that these properties actually characterize them. This characterization immediately implies the explicit form of Kazhdan’s theorem on the conjugation of Shimura varieties. As a further corollary, we show that each Shimura variety corresponding to an adjoint group has a canonical model over its re...

We study a canonical model of reputation between a long-run player and a sequence of short-run opponents, in which the long-run player is privately informed about an uncertain state, which determines the monitoring structure in the reputation game. The long-run player plays a stage-game repeatedly against a sequence of short-run opponents. We present necessary and sufficient conditions (on the ...

In this paper, we initiate our investigation of log canonical models for (Mg, αδ) as we decrease α from 1 to 0. We prove that for the first critical value α = 9/11, the log canonical model is isomorphic to the moduli space of pseudostable curves, which have nodes and cusps as singularities. We also show that α = 7/10 is the next critical value, i.e., the log canonical model stays the same in th...

Mumford defined a natural isomorphism between the intermediate jacobian of a conicbundle over P and the Prym variety of a naturally defined étale double cover of the discrminant curve of the conic-bundle. Clemens and Griffiths used this isomorphism to give a proof of the irrationality of a smooth cubic threefold and Beauville later generalized the isomorphism to intermediate jacobians of odd-di...

in financial distress studies selection of variable is commonly basedon the success of variables in variable sets employed in earlierbankruptcy studies, suggestions in the literature or an accompanyingdata reduction in a large set of variables. if seemingly different variablesets exhibit a strong relationship then heterogeneous variable setscapture common information. canonical correlation anal...

We prove that families of Prym varieties abelian Galois covers P1 in Ag do not give rise to high dimensional Shimura subvareties. This contributes the classification such totally geodesic subvarieties locus and extends results E. Colombo et al. which deal with 1-parameter families. Our method is based on analyzing Monodromy family.

We show that the Prym map for 4-th cyclic étale covers of curves of genus 4 is a dominant morphism to a Shimura variety for a family of Abelian 6-folds of Weil type. According to the result of Schoen, this implies algebraicity of Weil classes for this family.

In this paper we construct a non-trivial element in the higher Griffiths group Grif f 3,2 for the generic abelian fourfold A 4 with polarization of type (1, 2, 2, 2). The key idea is to use that A 4 can be realized as a generalized Prym variety and for this reason contains in a natural way some curves i.e. dimension 1 cycles.

This paper gives a uniform construction of infinitely many primitive Teichmüller curves V ⊂ Mg for g = 2, 3 and 4.