اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدSpecial families of curves, of Abelian varieties, and of certain minimal manifolds over curves
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This survey article discusses some results on the structure of families f:V-->U of n-dimensional manifolds over quasi-projective curves U, with semistable reduction over a compactification Y of U. We improve the Arakelov inequality for the direct images of powers of the dualizing sheaf. For families of Abelian varieties we recall the characterization of Shimura curves by Arakelov equalities. For families of curves we recall the characterization of Teichmueller curves in terms of the existence of certain sub variation of Hodge structures. We sketch the proof that the moduli scheme of curves of genus g>1 can not contain compact Shimura curves, and that it only contains a non-compact Shimura curve for g=3.
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Given an open subset U of a projective curve Y and a smooth family f:V-->U of curves, with semi-stable reduction over Y, we show that for a sub variation of Hodge structures of rank >2 the Arakelov inequality must be strict. For families of n-folds w
e prove a similar result under the assumption that the (n,0) component of the Higgs bundle defines fibrewise a birational map.
A fine moduli space is constructed, for cyclic-by-$mathsf{p}$ covers of an affine curve over an algebraically closed field $k$ of characteristic $mathsf{p}>0$. An intersection of finitely many fine moduli spaces for cyclic-by-$mathsf{p}$ covers of af
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Let $f:X to mathbb{P}^1$ be a non-isotrivial family of semi-stable curves of genus $ggeq 1$ defined over an algebraically closed field $k$ with $s_{nc}$ singular fibers whose Jacobians are non-compact. We prove that $s_{nc}geq 5$ if $k=mathbb C$ and
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Let $C$ be a nodal curve, and let $E$ be a union of semistable subcurves of $C$. We consider the problem of contracting the connected components of $E$ to singularities in a way that preserves the genus of $C$ and makes sense in families, so that thi
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These are notes of my lectures at the summer school Higher-dimensional geometry over finite fields in Goettingen, June--July 2007. We present a proof of Tates theorem on homomorphisms of abelian varieties over finite fields (including the $ell=p$ c
ase) that is based on a quaternion trick. In fact, a a slightly stronger version of those theorems with finite coefficients is proven.
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