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Jaya N. N. Iyer 《Mathematische Zeitschrift》2008,260(1):61-76
In this note, we investigate the cycle class map between the rational Chow groups and the arithmetic Deligne cohomology, introduced
by Green–Griffiths and Asakura–Saito. We show nontriviality of the Chern classes of flat bundles in the arithmetic Deligne
Cohomology in some cases and our proofs also indicate that generic flat bundles can be expected to have nontrivial classes.
This provides examples of non-zero classes in the arithmetic Deligne cohomology which become zero in the usual rational Deligne
cohomology. 相似文献
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Adrian Langer 《Mathematische Zeitschrift》2000,235(3):591-614
We define Chern classes of reflexive sheaves using Wahl's relative local Chern classes of vector bundles. The main result of the paper bounds contributions of singularities of a sheaf to the Riemann–Roch formula. Using it we are able to prove inequality in Wahl's conjecture on relative asymptotic RR formula for rank 2 vector bundles. Moreover, we prove that if Wahl's conjecture is true for a singularity then it is true for any its quotient. This implies Wahl's conjecture for quotient singularities and for quotients of cones over elliptic curves. Received March 2, 1998; in final form March 24, 1999 / Published online September 14, 2000 相似文献
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C. B. Thomas 《Mathematische Annalen》1971,190(4):323-328
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We develop an integral version of Deligne cohomology for smooth proper real varieties. For this purpose the role played by singular cohomology in the complex case has to be replaced by the ordinary bigraded Gal(mathbbC/mathbbR){Gal(mathbb{C}/{mathbb{R}})}-equivariant cohomology of Lewis et al. (Bull Am Math Soc (N.S.) 4(2):208–212, 1981), the equivariant counterpart of singular cohomology. The theory is aimed at giving more precise information about the 2-primary components of regulators. We establish basic properties and give a geometric interpretation for the groups in dimension 2 in weights 1 and 2. 相似文献
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Deligne cohomology can be viewed as a differential refinement of integral cohomology, hence captures both topological and geometric information. On the other hand, it can be viewed as the simplest nontrivial version of a differential cohomology theory. While more involved differential cohomology theories have been explicitly twisted, the same has not been done to Deligne cohomology, although existence is known at a general abstract level. We work out what it means to twist Deligne cohomology, by taking degree one twists of both integral cohomology and de Rham cohomology. We present the main properties of the new theory and illustrate its use with examples and applications. Given how versatile Deligne cohomology has proven to be, we believe that this explicit and utilizable treatment of its twisted version will be useful. 相似文献
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Oblatum 10-VII-1993 & 26-IX-1994 相似文献
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N. P. Strickland 《Topology》2001,40(6):1167-1216
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The main purpose of this paper is to generalize the celebrated L~2 extension theorem of Ohsawa and Takegoshi in several directions: The holomorphic sections to extend are taken in a possibly singular hermitian line bundle, the subvariety from which the extension is performed may be non reduced, the ambient manifold is K¨ahler and holomorphically convex, but not necessarily compact. 相似文献
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Johannes Huebschmann 《Archiv der Mathematik》1993,61(2):124-136
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Paolo Aluffi 《Transactions of the American Mathematical Society》1999,351(10):3989-4026
We prove a formula expressing the Chern-Schwartz-MacPherson class of a hypersurface in a nonsingular variety as a variation on another definition of the homology Chern class of singular varieties, introduced by W. Fulton; and we discuss the relation between these classes and others, such as Mather's Chern class and the -class we introduced in previous work.
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We construct the Chern character in the equivariant entire cyclic cohomology. We prove a general index theorem for theG-invariant Dirac operator.Supported in part by the Department of Energy under Grant DE-FG02-88ER25065. 相似文献
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