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Mathematician, researching in Algebraic Geometry and related topics.
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revised 
Smoothing transverse intersections
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revised 
Smoothing transverse intersections
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revised 
Smoothing transverse intersections
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answered  Smoothing transverse intersections 
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holomorphic curves invariant by lattices
If $n \geq 2$, there is in general no such a function. Indeed, the $\Lambda$invariant curve $C$ would give rise to a compact $1$dimensional submanifold in the complex torus $T = \mathbb{C}^n / \Lambda$, but it is known that for a general choice of the lattice such a torus contains no $1$dimensional complex submanifolds at all. So, your lattice must be special. For instance, you can require that the torus $T$ is algebraic (i.e, an abelian variety), which means that $\Lambda$ satisfies the Riemann bilinear conditions. 
Mar 23 
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Disjoint curves in an algebraic surface
@MarcoGolla: do you have a reference? 
Mar 23 
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Disjoint curves in an algebraic surface
Donaldson's theorem concerns simply connected 4manifolds. However, there are (non rational) complex surfaces with $p_g=q=0$ that are not simply connected (for instance, the classical Godeaux surface), so in this case I do not see how to conclude that the intersection form must be necessarily diagonalisable. I'm missing something? 
Mar 20 
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Continuous maps which send intervals of $\mathbb{R}$ to convex subsets of $\mathbb{R}^2$
I'm far for being an expert so I'm not sure whether this makes sense, anyway did you try to build a counterexample by using some kind of planefilling curve? 
Mar 19 
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Relative tangent space to proper morphism and irreducibility of fibers
Some authors require irreducibility in the definition of variety (e.g, Hartshorne), but some others do not (e.g, Shafarevich), so it is better to specify. 
Mar 19 
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Relative tangent space to proper morphism and irreducibility of fibers
So, are you assuming that $X_y$ is a connected, nonsingular variety? 
Mar 16 
revised 
Singular models of K3 surfaces
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Mar 16 
revised 
Singular models of K3 surfaces
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Mar 16 
answered  Singular models of K3 surfaces 
Mar 13 
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Covering of schemes and flatness
The normalization of the cuspidal curve is actually bijective (in fact, it is a homeomorphism), but the fibre over the cusp is not reduced. 
Mar 13 
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Analytically but not algebraically smoothable singularity
Right, thanks. Corrected (and reference added). 
Mar 13 
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Analytically but not algebraically smoothable singularity
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Mar 13 
answered  Analytically but not algebraically smoothable singularity 
Mar 2 
awarded  Good Answer 
Mar 2 
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Residual finiteness: why do we care?
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Feb 27 
awarded  Nice Answer 