کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4665170 | 1633794 | 2016 | 25 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: An analytic Grothendieck Riemann Roch theorem An analytic Grothendieck Riemann Roch theorem](/preview/png/4665170.png)
We extend the Boutet de Monvel Toeplitz index theorem to complex manifolds with isolated singularities following the relative K -homology theory of Baum, Douglas, and Taylor for manifolds with boundary. We apply this index theorem to study the Arveson–Douglas conjecture. Let BmBm be the unit ball in CmCm, and I an ideal in the polynomial algebra C[z1,⋯,zm]C[z1,⋯,zm]. We prove that when the zero variety ZIZI is a complete intersection space with only isolated singularities and intersects with the unit sphere S2m−1S2m−1 transversely, the representations of C[z1,⋯,zm]C[z1,⋯,zm] on the closure of I in La2(Bm) and also the corresponding quotient space QIQI are essentially normal. Furthermore, we prove an index theorem for Toeplitz operators on QIQI by showing that the representation of C[z1,⋯,zm]C[z1,⋯,zm] on the quotient space QIQI gives the fundamental class of the boundary ZI∩S2m−1ZI∩S2m−1. In the appendix, we prove with Kai Wang that if f∈La2(Bm) vanishes on ZI∩BmZI∩Bm, then f is contained inside the closure of the ideal I in La2(Bm).
Journal: Advances in Mathematics - Volume 294, 14 May 2016, Pages 307–331