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bio website www2.imperial.ac.uk/~rpanneko
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I am a postdoc at Imperial College. My interests are rational points on varieties, in particular K3 surfaces and abelian varieties.


1d
revised Is any quadric birational to a product of Brauer-Severi varieties?
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revised Is any quadric birational to a product of Brauer-Severi varieties?
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comment Is any quadric birational to a product of Brauer-Severi varieties?
Thank you for the question! It seems that the same argument should work for any quadric $V$ over a number field that fails to have local points at exactly one place.
1d
revised Is any quadric birational to a product of Brauer-Severi varieties?
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revised Is any quadric birational to a product of Brauer-Severi varieties?
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1d
answered Is any quadric birational to a product of Brauer-Severi varieties?
1d
comment Can a non-surjective polynomial map from an infinite field to itself miss only finitely many points?
Does this generalize at all to maps $f_k \colon V(k) \rightarrow W(k)$, where $V,W$ are $k$-varieties (or $k$-schemes) and where $f_k$ is induced by a morphism $f \colon V \rightarrow W$? (And what if $f$ is a rational map?)
Apr
14
comment Find two triangles of longest side length 25?
It can be deduced from yours. Write $t = m/n$ with $m,n$ integers, then multiply the three side-lengths by $kn^2$ for an arbitrary integer $k$.
Apr
14
comment Find two triangles of longest side length 25?
Your parametrization only gives some Pythagorean triangles, not all. You should use $(a,b,c)=(k(m^2-n^2),2kmn,k(m^2+n^2))$, with $k,m,n$ integers.
Apr
14
comment Find two triangles of longest side length 25?
They are 15-20-25 and 7-24-25.
Apr
12
comment Quadratic twist of an elliptic curve given by non-Weierstrass model
I think joro is right: the isomorphism class of $E_d$ does not depend on the choice of origin on $E$. You see this by simply writing down the obvious $\overline{k}$-isomorphism between $E_d$ and $E_d'$ (which we define as the twist by the same cocycle but wrt some different choice of origin on $E$) and check that it is defined over $k$.
Apr
12
revised Quadratic twist of an elliptic curve given by non-Weierstrass model
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Apr
12
revised Quadratic twist of an elliptic curve given by non-Weierstrass model
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Apr
12
revised Quadratic twist of an elliptic curve given by non-Weierstrass model
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Apr
12
answered Quadratic twist of an elliptic curve given by non-Weierstrass model
Apr
9
comment Algebraic Geometry for non-mathematician
I always found the Harris book much more difficult than the two Shafarevich volumes. There are many examples in Harris's book, but there are also many claims that are left to the reader, and the prerequisites are quite substantial.
Mar
18
comment Picard number of Prym Variety
But how do you know that the desired conclusion is false for a generic curve $C$? Is this somehow related to the work of Maulik and Poonen (Néron-Severi groups under specialization)?
Mar
2
comment “Gross-Zagier” formulae outside of number theory
Are there examples where the class of $D \subset M \times M$ in the cohomology of $M \times M$ is trivial? (Since it has non-zero intersection number with $M \times \{ \operatorname{pt} \}$, I am tempted to think the answer can't be yes.)
Mar
1
comment Functoriality of Br(X)
There is no inclusion $X \rightarrow \overline{X}$, but there is a projection going the other way. :)
Feb
27
comment Consecutive square values of cubic polynomials
Very nice answer. By the way, the minus in one of the indices in your displayed formula should be a plus. (I deleted my previous comment, whose validity rested on the assumption that the $V_c$ are smooth. I thought I had an easy proof of this, but it was wrong.)