Reputation
33,824
Next tag badge:
117/100 score
18/20 answers
Badges
3 84 135
Newest
 Nice Answer
Impact
~327k people reached

37m
comment Picard groups of quartic K3 surfaces
It is possible to construct a K3 surface $S$ with Picard rank $2$ by taking a double cover of the plane of the form $w^2=F_6(x, \, y, \, z)$, where $F_6$ is a smooth plane sextic curve which admits a six-tangent conic. The surface $S$ does not sit naturally in $\mathbb{P}^4$, but in the weighted projective space $\mathbb{P}(1, \, 1, \, 1, \, 3)$. See Example 20 here: www-fourier.ujf-grenoble.fr/sites/ifmaquette.ujf-grenoble.fr/…
18h
answered Picard groups of quartic K3 surfaces
1d
comment Great Mathematicians Without a PhD
Starting from when? Otherwise, I could say Apollonius and Archimedes. Anyway, I do not think this question is suitable for MO.
Apr
29
comment Use of algebraic topology in geometry(differential and complex analytic)
This is an extremely broad question. There are hundred of situations where algebraic topology is useful for the study of geometry: monodromy of coverings, classifying spaces, characteristic classes, invariants of singularities, etc etc. It is really impossible to cover such a plenty of applications in a MathOverflow answer. Voting to close.
Apr
29
comment Early examples of problems that are easier in high dimension
"but here the 3D result does readily imply the 2D one" Yes, but only for some projective planes, namely the ones where you can perform this lifting construction to the $3$-space. In fact, Desargues theorem is valid in all projective spaces of dimension $\geq 3$, but there are some non-desarguesian projective planes. So the case of dimension $2$ is really the tricky part here. Is not this precisely an example of what you are looking for?
Apr
29
answered Which varieties are flat degenerations of projective space?
Apr
28
awarded  Nice Answer
Apr
28
revised Is this group given presentation isomorphic to $\mathbb{Z}_2$, and why?
added 34 characters in body
Apr
28
answered General Reference for surface singularities
Apr
27
comment Can the matrix exponential be equal to the elementwise exponential
oops, right :-)
Apr
27
comment Can the matrix exponential be equal to the elementwise exponential
How does your argument rule out a $2\times 2$ diagonal matrix?
Apr
27
comment Question regarding Geometric meaning of Noether normalization theorem for projective varieties
Have a look at Emerton's answer in this thread: mathoverflow.net/questions/42275/…
Apr
22
comment Calabi-Yau with nodes
A hypersurface singularity is always Gorenstein, and it is normal as soon as it is of codimension at least $2$.
Apr
22
revised Chern classes of ideal sheaf of an analytic subset
edited body
Apr
21
revised Equivalence of Branched Coverings
deleted 3 characters in body
Apr
21
answered “Smooth” rationally connectivity
Apr
20
comment Self-intersection of a Cartier divisor
Yes, under your assumptions the movable part $M$ of $|D|$ is necessarily composed with a base-point free rational pencil, hence $M^2=0$.
Apr
20
revised Self-intersection of a Cartier divisor
added 6 characters in body; edited title
Apr
20
revised Self-intersection of a Cartier divisor
added 35 characters in body
Apr
20
revised Self-intersection of a Cartier divisor
added 35 characters in body