14 research outputs found
PU(2) monopoles. II: Top-level Seiberg-Witten moduli spaces and Witten's conjecture in low degrees
In this article we complete the proof---for a broad class of
four-manifolds---of Witten's conjecture that the Donaldson and Seiberg-Witten
series coincide, at least through terms of degree less than or equal to c-2,
where c is a linear combination of the Euler characteristic and signature of
the four-manifold. This article is a revision of sections 4--7 of an earlier
version, while a revision of sections 1--3 of that earlier version now appear
in a separate companion article (math.DG/0007190). Here, we use our
computations of Chern classes for the virtual normal bundles for the
Seiberg-Witten strata from the companion article (math.DG/0007190), a
comparison of all the orientations, and the PU(2) monopole cobordism to compute
pairings with the links of level-zero Seiberg-Witten moduli subspaces of the
moduli space of PU(2) monopoles. These calculations then allow us to compute
low-degree Donaldson invariants in terms of Seiberg-Witten invariants and
provide a partial verification of Witten's conjecture.Comment: Journal fur die Reine und Angewandte Mathematik, to appear; 65 pages.
Revision of sections 4-7 of version v1 (December 1997
Local properties and Hilbert schemes of points
Alexander Grothendieck's concepts turned out to be astoundingly powerful and productive, truly revolutionizing algebraic geometry. He sketched his new theories in talks given at the Seminaire Bourbaki, between 1957 and 1962. He, then, collected these lectures in a series of articles in "Fondements de la geometrie algebrique" (commonly known as "FGA"). Much of "FGA" is now common knowledge. However, some of it is less well-known, and only a few geometers are familiar with its full scope. The goal of the current book, which resulted from the 2003 Advanced School in Basic Algebraic Geometry (Trieste, Italy), is to fill in the gaps in Grothendieck's very condensed outline of his theories. The four main themes discussed in the book are descent theory, Hilbert and Quot schemes, the formal existence theorem, and the Picard scheme. The authors present complete proofs of the main results, using newer ideas to promote understanding whenever necessary, and drawing connections to later developments. With the main prerequisite being a thorough acquaintance with basic scheme theory, this book is a valuable resource for anyone working in algebraic geometry
Euler number of the compactified Jacobian and multiplicity of rational curves
In this paper we show that the Euler number of the compactified Jacobian J\u304C of a rational curve C with locally planar singularities is equal to the multiplicity of the (\u3b4-constant stratum in the base of a semi-universal deformation of C. The number e(J\u304C) is the multiplicity assigned by Beauville to C in his proof of the formula, proposed by Yau and Zaslow, for the number of rational curves on a K3 surface X. We prove that e(J\u304C) also coincides with the multiplicity of the normalisation map of C in the moduli space of stable maps to X
Validation of satellite land surface temperature products using ground-based measurements and heritage satellite data â Protocol, limitations and results
National audienc
Validation of satellite land surface temperature products using ground-based measurements and heritage satellite data â Protocol, limitations and results
National audienc
Validation of satellite land surface temperature products using ground-based measurements and heritage satellite data â Protocol, limitations and results
National audienc