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Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.
1
vote
Accepted
A condition on isolated singularity
Assume that $F$ is quasihomogeneous.
A condition on $F$ would be the following.
For each $k$ write $F=x_kG+H_k(x_1,\dots,x_{k-1},x_{k+1},\dots, x_N)$. Then $H_k$ is quasihomogeneous.
If for each $k$ …
1
vote
The locus of rational/elliptic curves on a special surface in $\mathbb{P}^3$
There are results by Voisin (On a conjecture of Clemens on rational curves on hypersurfaces Journal of Differential Geometry 44 (1996) 200-214) and Ulmer (Rational curves on elliptic surfaces, arXiv:1 …