By Prof. Dr. Gennadi M. Henkin, Prof. Dr. Jürgen Leiterer (auth.)

ISBN-10: 0817634134

ISBN-13: 9780817634131

ISBN-10: 1489967249

ISBN-13: 9781489967244

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**Extra resources for Andreotti-Grauert Theory by Integral Formulas**

**Example text**

N, the sequence of sheaves is exact. , s be the corresponding long exact cohomology sequence. 23), it follows that, for s=1, ... 24), we see that the Hr(X,(Z~ 0 )E) and Hr-n(X,(Z~n)E) are isomorphic. 26) this. implies that, for r~n+1, Hr(X,OE) is isomorphic to Hr-n(X,(C~n)E). 18). For the remainder of this proof we may assume that 1

YN) a frame forD, and SK=SK(Y). A Leray map for (D,Y) (or for D) is, by definition, a map v which attaches to each strictly increasing collection K=(k 1 , ... ,k 1 ) of inte· 1 n 1 n . gers 1~~ 1 < ... ,vK) def1ned for zED, x£SK 1 and t~~K such that, for any collection K=(k 1 , ... ,k 1 ) of strictly increasing integers 1Sk 1<... 5) A Leraydatumfor (D, Y) (or for D) is, by definition, a family N w={w j} j= 1 of Q! 1 n -valued C maps defined for all z~D and X€Sj such that for all z'D and 48 x~Sj ( j=l, ...

Let D ~ Cn be a domain with almost c1 boundary, and let v be a Leray map for D. 6) and n-1 = -1- det ( v 0 (z,x,t), r---0----,) (3 +dt)v (z,x,t) I\6J(x). 7) (x,t)£aDx[0,1J we define a continuous differential form Rvf in D. Av Av By Rr=Rr(z,x,t) (r=O, ... ,n-1) we denote the sum of all monomials in Rv which are of bidegree (O,r) in z. 6) for r=O, ... , n-1. 5. Proposition. Let D cc Cn be a domain with almost c1 boundary, and let v be a Leray map for D. 9) 1~r~n-1 (x,thaDx[O, 1] and Rvf = 0 if r=O or r=n.

### Andreotti-Grauert Theory by Integral Formulas by Prof. Dr. Gennadi M. Henkin, Prof. Dr. Jürgen Leiterer (auth.)

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