Affiliation:
1. Department of Mathematics, University of California San Diego, 9500 Gilman Drive # 0112, La Jolla, CA 92093-0112,USA
Abstract
AbstractWe present a proof that
for any Hodge isometry {\psi\colon\hskip-0.853583ptH^{2}(S_{1},{\mathbb{Q}})\hskip-0.853583pt%
\rightarrow\hskip-1.13811ptH^{2}(S_{2},{\mathbb{Q}})} between any two
Kähler {K3} surfaces {S_{1}} and {S_{2}} we can
find a finite sequence of K3 surfaces and analytic (2,2)-classes
supported on successive products, such that the isometry ψ is the
convolution of these classes.
The proof of this fact implies that for projective {S_{1},S_{2}} the class of ψ is algebraic.
This proves a conjecture
of I. Shafarevich [26].
Subject
Applied Mathematics,General Mathematics
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