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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
1
vote
approaches to Apollonius circle problems
Two circles with different radii can also be mapped to two circles with the same radius by an inversion (or a möbius transformation in general). Then the family of tangent circles is easier to describ …
5
votes
Accepted
Two limit cycles which lie on the same leaf
Possibly a very "brute force" approach could be the following. Take an non-singular algebraic curve $H(x,y)=0$ given by a polynomial $H(x,y)$ with real coefficients that has at least two ovals in the …
2
votes
Accepted
Question on Weil-Petersson metric on Teichmuller space
One way to define Teichmueller space is to fix a Riemann surface
$X$, with a fixed complex structure, and define the space of all
Beltrami differentials $\mathcal{M}(X)$ on $X$. Notice that in
this wa …