Related papers: A calculus for shadows of smooth 4-manifolds

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This paper has been withdrawn by the author due to a error in attachment of source file.

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This paper has been withdrawn by the author due to an error in the proof of Theorem 6.

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This paper has been withdrawn by the author due to an error in the sufficient condition given for the proof of the Tate conjecture for Catanese surfaces.

We prove the vanishing of many Welschinger invariants of real symplectic $4$-manifolds. In some particular instances, we also determine their sign and show that they are divisible by a large power of 2. Those results are a consequence of…

This paper has been withdrawn by the author, due to obsolete reference [4], insufficient discussion in sec. 4, and major conceptual error in sec. 5.

The paper is withdrawn by the author due to a recently discovered flaw in a basic proof.

The paper is withdrawn because the analysis appeared to be incomplete.

This paper has been withdrawn by the authors due to crucial error in the main proof (located in Section 2.4). The authors apologize for any inconveniences.

This paper has been withdrawn by the author(s), due to a crucial error in eq. 6.

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This paper has been withdrawn by the author due to a crucial error in the definition of homomorphism.

This paper has been withdrawn by the authors, due to a flaw in the proof of Theorem 1. This preprint is superseded by quant-ph/0610027, where a correct proof can be found. Thanks to Rainer Siegmund-Schultze for spotting the error.

Paper withdrawn by the author.

This paper has been withdrawn by the authors, as it contains some errors. The core of it has been entirely rewritten in math.FA/0510454.