https://grishataroyan.org/tags/toric-geometry/Recent content in Toric Geometry on Grisha TaroyanHugoen-USThu, 16 Jul 2026 00:00:00 -0400https://grishataroyan.org/blog/no-submanifolds/Thu, 16 Jul 2026 00:00:00 -0400https://grishataroyan.org/blog/no-submanifolds/<div class="compiled-latex"> <h2 class='likesectionHead' id='contents'> <a id='x1-1000'></a>Contents</h2> <div class='tableofcontents'> <span class='sectionToc'><span class='toc-number' aria-hidden='true'>1</span><a href='#why-i-decided-to-write-this-post' id='QQ2-1-2'>Why I decided to write this post</a></span> <br /> <span class='sectionToc'><span class='toc-number' aria-hidden='true'>2</span><a href='#complex-tori-and-abelian-surfaces' id='QQ2-1-3'>Complex tori and abelian surfaces</a></span> <br /> <span class='sectionToc'><span class='toc-number' aria-hidden='true'>3</span><a href='#an-explicit-example' id='QQ2-1-4'>An explicit example</a></span> <br /> <span class='sectionToc'><span class='toc-number' aria-hidden='true'>4</span><a href='#why-this-example-is-generic' id='QQ2-1-5'>Why this example is generic</a></span> <br /> <span class='sectionToc'><span class='toc-number' aria-hidden='true'></span><a href='#references' id='QQ2-1-6'>References</a></span> </div> <h2 class='sectionHead' id='why-i-decided-to-write-this-post'><span class='titlemark'>1 </span> <a id='x1-20001'></a>Why I decided to write this post</h2> <p class='noindent'>This post (as most others in this blog will be) is an example that I have to recall quite often, but can never remember the details. On one hand, it is a very simple example, on the other hand, it shows a huge difference between the algebraic and complex geometry. For instance, it shows that some naïve analogies between algebraic and holomorphic “toric” geometries can not literally be true. In particular, it shows how the relationship between Cartier divisors and line bundles breaks down in the non-algebraic case. </p>