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1. The sum of Lyapunov exponents on Quadradic differentials | |||
YU Fei | |||
Mathematics 26 May 2017 | |||
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Abstract:In this paper we reporve a Kontsevich-Zorich formula for the sum of Lyapunov exponents of Teichm"{u}ller curves on Quadradic differentials. For a Teichm"{u}ller curve in moduli space of abelian differentials. Under some additionalassumptions, we also get an upper bound of individual Lyapunov exponents; in particular we get Lyapunov exponents in hyperelliptic loci and low genusnon-varying strata. | |||
TO cite this article:YU Fei. The sum of Lyapunov exponents on Quadradic differentials[OL].[26 May 2017] http://en.paper.edu.cn/en_releasepaper/content/4736255 |
2. Upper bounds of the sum of Lyapunov exponents on Teichmüller curves | |||
YU Fei | |||
Mathematics 08 May 2017 | |||
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Abstract:We get anupper bound of the slope of each graded quotient for theHarder-Narasimhan filtration of the Hodge bundle of a Teichmüller curve. As an application, we show that the sum ofLyapunov exponents of a Teichmüller curve does not exceed${(g+1)}/{2}$, with equality reached if and only if the curve liesin the hyperelliptic locus induced from$mathcal{Q}(2k_1,...,2k_n,-1^{2g+2})$ or it is some specialTeichm"{u}ller curve in $Omegamathcal{M}_g(1^{2g-2})$. | |||
TO cite this article:YU Fei. Upper bounds of the sum of Lyapunov exponents on Teichmüller curves[OL].[ 8 May 2017] http://en.paper.edu.cn/en_releasepaper/content/4733747 |
3. Strongly Liftable Schemes and the Kawamata-Viehweg Vanishing in Positive Characteristic II | |||
Xie Qihong | |||
Mathematics 13 December 2012 | |||
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Abstract:A smooth scheme X over a field k of positive characteristic is said to be strongly liftable, if X and all prime divisors on X can be lifted simultaneously over W2(k). In this paper, first the author proves that smooth toric varieties are strongly liftable, hence the Kawamata-Viehweg vanishing theorem holds for smooth projective toric varieties. Second, the author proves the Kawamata-Viehweg vanishing theorem for normal projective surfaces which are birational to a strongly liftable smooth projective surface. Finally, the author deduces the cyclic cover trick over W2(k), which can be used to construct a large class ofliftable smooth projective varieties. | |||
TO cite this article:Xie Qihong. Strongly Liftable Schemes and the Kawamata-Viehweg Vanishing in Positive Characteristic II[OL].[13 December 2012] http://en.paper.edu.cn/en_releasepaper/content/4503779 |
4. Strongly Liftable Schemes and the Kawamata-Viehweg Vanishing in Positive Characteristic I | |||
Xie Qihong | |||
Mathematics 13 December 2012 | |||
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Abstract:A smooth scheme X over a field k of positive characteristic is said to be strongly liftable, if X and all prime divisors on X can be lifted simultaneously over W2(k). Some concrete examples and properties of strongly liftable schemes are given in this paper. As an application, the author proves that theKawamata-Viehweg vanishing theorem in positive characteristic holds on any normal projective surface which is birational to a strongly liftable surface. | |||
TO cite this article:Xie Qihong. Strongly Liftable Schemes and the Kawamata-Viehweg Vanishing in Positive Characteristic I[OL].[13 December 2012] http://en.paper.edu.cn/en_releasepaper/content/4503770 |
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