By Spencer J. Bloch, I. Dolgachev, W. Fulton

This quantity comprises the complaints of a joint USA-USSR symposium on algebraic geometry, held in Chicago, united states, in June-July 1989.

**Read Online or Download Algebraic Geometry: Proceedings of the U. S.-U. S. S. R. Symposium Held in Chicago, June 20-July 14, 1989 PDF**

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**Additional info for Algebraic Geometry: Proceedings of the U. S.-U. S. S. R. Symposium Held in Chicago, June 20-July 14, 1989**

**Example text**

Peters, Automorphisms of Enriques surfaces, Inv. Math. 73 (1983), 383-411. F. C o s s e c , I. Dolgachev, Enriques surfaces I. Birkhauser. 1989 F. C o s s e c , 1. Dotgachev, Enriques surfaces II (in preparation). F. C o s s e t , Reye congruences, Trans. Amer. Math. Soc. 280 (1983), 737-751. A. Conte, A. (to appear in Trans. Amer. Math. ) H. Kim, Vector bundles on Enriques surfaces. D. thesis. Univ. of Mich. 1990. S. Kuloshov, A theorem on existence of exceptional bundles on surfaces of type K3, Izv.

Let E be a rank 2 vector bundle on an Enriques surface S with q ( E ) = A and ~ ( E ) = 3. The following assertions are equivalent: (i) E is A-semi-stable; (ii) E is isomorphic to the Reye bundle. (iii) E is A-stable. PROOF. (i) ~ (ii) By Proposition 1, h°(E) ;~ 0. We may assume that the zero set of any non-zero section 46 has a l - d i m e n s i o n a l part D. Otherwise E is regular, and the semi-stability implies that case (iii) of Theorem 2 m u s t hold. Consider the exact sequence 0 - o (gs(D) -o E --o 9Z(A-D) --o 0.

Let T Y= U X r be the corresponding r~T Define a sheaf ~X,Y) as the closed subvariety in X=X. intersection of the sheaves From of ~, and > ~ we A-module see ), r~T. that the sheaf Q~X,Y) is 29 ~,T) = ~ ~,T)(m)xm' where n ~ , T ) (m) = { ~ ( m ) , In particular, from if if m~reTUr, 0 consists T=a~ otherwise. of all faces of ~ different ~, then n~'0~)(m) = { AP(Me)'O otherwise,if meInt(~), and we have the canonical isomorphism 0 n~X,y ) = n(X,y)®AP(Mc). 8. toric X-Y Proposition. varieties. strata of on X, ~:X Let Let and X-Y.