All Questions

I seem to remember that a K3 surface with big Picard rank always has smooth rational curves. This question is equivalent to the following question about integral quadratic lattices. Let us call a ...

Let $\Lambda$ be a non-degenerate lattice (over $\mathbb{Z}$) with quadratic form $q$. I define the spinor norm $\theta \colon O(\Lambda_\mathbb{R} )\to \lbrace\pm 1\rbrace$ as follows: For a ...

I have a bivariate modular polynomial of shape $$f(x,y)=x^2y-g(x)\equiv 0\bmod q$$ where $q=(2p-1)(2p+1)$ is a product of two primes $2p-1$ and $2p+1$, $g(x)\in\mathbb Z[x]$ is of degree four and $f(...

Let $p$ be odd prime and $\mathbb Q_p$ be the $p$-adic field. Consider the field extension $K=\mathbb Q_p(\sqrt[(p^5-1)]{p^2})$ of $\mathbb Q_p$ of degree $\frac{p^5-1}{2}$. My question: I want see ...

Consider three lattices $L_1$, $L_2$ in $\Bbb Z^{n+1}$ and $L$ in $\Bbb Z^{2n+1}$. Let $L_1+v_1$, $L_2+v_2$ and $L+v$ be their respective translationsfor some $v_1,v_2\in\Bbb Z^{n+1}\backslash\{(0,\...

Anyone who likes $K3$ surfaces cares about lattices of the form $$ (2d)\cdot y^2 - 2x \cdot z$$ (namely the mukai pairing on $H^*_{alg}(K3)$ of picard $1$ with polarization $d$). Inside we have ...