摘要翻译:
研究曲线雅可比上的重言圈类。我们证明了关于一般曲线上重言类环的一个新结果,该结果允许除其他外,易于维数计算,并导致了关于该环结构的一些一般结果。其次,我们得到了某些生成类P_i的一个消失结果;这改进了Herbaut先前的一个结果。最后,我们将Herbaut和van der Geer-Kouvidakis的一个结果推广到Chow环(与它的商模代数等价性相反),并给出了进一步得到显式圈关系的方法。作为其中的一个组成部分,我们证明了关于Polishchuk算子D如何提升到Chow(J)的重言子代数的一个定理。
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英文标题:
《Relations between tautological cycles on Jacobians》
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作者:
Ben Moonen
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最新提交年份:
2007
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分类信息:
一级分类:Mathematics 数学
二级分类:Algebraic Geometry 代数几何
分类描述:Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇,叠,束,格式,模空间,复几何,量子上同调
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英文摘要:
We study tautological cycle classes on the Jacobian of a curve. We prove a new result about the ring of tautological classes on a general curve that allows, among other things, easy dimension calculations and leads to some general results about the structure of this ring. Next we obtain a vanishing result for some of the generating classes p_i; this gives an improvement of an earlier result of Herbaut. Finally we lift a result of Herbaut and van der Geer-Kouvidakis to the Chow ring (as opposed to its quotient modulo algebraic equivalence) and we give a method to obtain further explicit cycle relations. As an ingredient for this we prove a theorem about how Polishchuk's operator D lifts to the tautological subalgebra of Chow(J).
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PDF链接:
https://arxiv.org/pdf/0706.3478