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Mathematician, researching in Algebraic Geometry and related topics.


2h
comment Find all solutions in positive integers of the diophantine equation $w^2+x^2+y^2=z^2$
Hint: sthereographic projection. So said, I'm voting to close since this is not a research-level question.
2d
comment singular point of a complete intersection surface
Of course. Let $H_1 \subset \mathbb{P}^3$ be a smooth quadric surface and $H_2$ a tangent plane to $H_1$. Then $H_1 \cap H_2$ is a pair of intersecting lines. See Roy's answer below.
Nov
21
revised Computing the nonsingular projective model of a plane curve
edited body
Nov
21
answered Computing the nonsingular projective model of a plane curve
Nov
17
revised When is a surface in a threefold contractible to a curve?
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Nov
17
comment When is a surface in a threefold contractible to a curve?
@ArtiePrendergast-Smith: Right, my answer only considers extremal contractions. I corrected it. Thanks for the remark.
Nov
15
comment Reference request for cohomology of coverings
But why are you sure that this is true in such a generality?
Nov
15
awarded  Enlightened
Nov
15
awarded  Nice Answer
Nov
15
revised Curves on varieties, and a criterion for nef divisor
improved formatting
Nov
12
comment Two (other) rings…are they isomorphic?
Anyway, already for isolated singularities, it is not true in general that the analytic (or formal) type of the singularity is the same of the type of the tangent cone. For instance, take $$\mathbb{C}[[x, y, z, w]]/(x^3+y^3+z^3+w^3), \quad \mathbb{C}[[x, y, z, w]]/(x^3+y^3+z^3+w^3+xyzw).$$ Then these two germs are not isomorphic: in fact they have the same Milnor number ($16$) but different Tjurina number ($16$ and $15$, respectively).
Nov
12
comment Two (other) rings…are they isomorphic?
Just a remark: in this case, the singularities of your hypersurfaces at the origin are not isolated.
Nov
12
comment Does some square of the first Chern class preserved by conifold transition?
See Corti-Smith: Conifold transitions and Mori Theory, Corollary 2. intlpress.com/site/pub/pages/journals/items/mrl/content/vols/…
Nov
12
comment Two rings…are they isomorphic?
I completely agree with Vladimir Dotsenko.
Nov
7
revised Embedding proper algebraic spaces
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Nov
7
revised Embedding proper algebraic spaces
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Nov
7
answered Embedding proper algebraic spaces
Nov
7
comment Embedding proper algebraic spaces
Are you sure that this exclude the possibility of embedding $S$ into a smooth algebraic space? It seems to me that this argument only works if $X$ is a scheme, or I am missing something?
Nov
7
awarded  Nice Answer
Nov
7
revised When is a surface in a threefold contractible to a curve?
added 145 characters in body