Develops a computer-aided symplectic Cremona transformation technique to study surface configurations in rational 4-manifolds and gives an independent proof that Fano plane line arrangements cannot exist symplectically.
Pseudoholomorphic curves and the symplectic isotopy problem
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abstract
The deformation problem for pseudoholomorphic curves and related geometrical properties of the total moduli space of pseudoholomorphic curves are studied. A sufficient condition for the saddle point property of the total moduli space is established. The local symplectic isotopy problem is formulated and solved for the case of imbedded pseudoholomorphic curves. It is shown that any two symplectically imbedded surfaces Sigma_0, Sigma_1 in CP^2 of the same degree d\le 6 are symplectically isotopic.
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math.SG 1years
2025 1verdicts
UNVERDICTED 1representative citing papers
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Symplectic configurations: a homological and computer-aided approach
Develops a computer-aided symplectic Cremona transformation technique to study surface configurations in rational 4-manifolds and gives an independent proof that Fano plane line arrangements cannot exist symplectically.