By Piotr Pragacz

ISBN-10: 3764385367

ISBN-13: 9783764385361

ISBN-10: 3764385375

ISBN-13: 9783764385378

The articles during this quantity are committed to:

- moduli of coherent sheaves;

- crucial bundles and sheaves and their moduli;

- new insights into Geometric Invariant Theory;

- stacks of shtukas and their compactifications;

- algebraic cycles vs. commutative algebra;

- Thom polynomials of singularities;

- 0 schemes of sections of vector bundles.

The major function is to offer "friendly" introductions to the above subject matters via a sequence of complete texts ranging from a truly straightforward point and finishing with a dialogue of present learn. In those texts, the reader will locate classical effects and techniques in addition to new ones. The publication is addressed to researchers and graduate scholars in algebraic geometry, algebraic topology and singularity thought. lots of the fabric awarded within the quantity has now not seemed in books before.

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**Extra info for Algebraic cycles, sheaves, shtukas, and moduli**

**Example text**

Let E be a coherent sheaf on Cn . We say that E is quasi free at P if EP is quasi free, and that E is quasi locally free if it is quasi free at every point of C. 6. The On,P -module M is quasi free if and only if Gr(M ) is a free OC,P -module, if and only if all the Mi /Mi+1 are free OC,P -modules. It follows that the set of points P ∈ C such that E is quasi free at P is open and nonempty, and that E is quasi locally free if and only if Gr(E) is a vector bundle on C, if and only if all the Ei /Ei+1 are vector bundles on C.

It has a ﬁne moduli space M which is canonically isomorphic to P(F surj ) ×M×N ×Z P(G surj ). -M. 3. Examples We give two examples of ﬁne moduli spaces of wide extensions on P3 . , null correlation bundles. It is canonically isomorphic to an open subset of P5 . 1. Rank 3 bundles. Let n > 4 be an integer. We consider wide extensions 0 −→ E(n) −→ E −→ I −→ 0 where E ∈ MP3 (0, 1), is a line in P3 and I its ideal sheaf. The bundle E has rank 3 and Chern classes 2n, n2 + 2, 2n + 2. 1 that the set of such extensions admits a ﬁne moduli space M of dimension 2n + 14.

Memoirs of the Amer. Math. , Vol. 29, N. 238 (1981). [21] Yoshioka, K. A note on the universal family of moduli of stable sheaves. Journ. Reine Angew. Math. 496 (1998), 149–161. fr/~drezet Algebraic Cycles, Sheaves, Shtukas, and Moduli Trends in Mathematics, 33–43 c 2007 Birkh¨ auser Verlag Basel/Switzerland Moduli Spaces of Coherent Sheaves on Multiples Curves Jean-Marc Dr´ezet 1. Introduction Let S be a projective smooth irreducible surface over C. The subject of this paper is the study of coherent sheaves on multiple curves embedded in S.

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