0
$\begingroup$

Should there be another tag for vector bundles in Algebraic geometry (over schemes)?

Some questions about vector bundles in the sense of algebraic geometry are given the tag whose tag description says

A continuously varying family of vector spaces of the same dimension over a topological space. If the vector spaces are one-dimensional, the term line bundle is used and has the associated tag line-bundles.

So, the question is, is it a better idea to create another tag for vector bundles in the sense of algebraic geometry?

$\endgroup$
  • 1
    $\begingroup$ I agree with S. Carnahan's answer. Multiplication of tags is results in a less coherent use and sets up artificial boundaries (differential and algebraic geometry are not disjoint settings). I'd even say that the fact the tag vector-bundles is transversal to those subjects makes it valuable. That some people reading the tag vector-bundles have difficulty with understanding those posts in algebraic geometry is part of the game. $\endgroup$ – YCor Oct 5 at 6:24
  • $\begingroup$ @YCor “That some people reading the tag vector-bundles have difficulty with understanding those posts in algebraic geometry is part of the game”.. thank you.. :) every time you respond, it teach me something.. $\endgroup$ – Praphulla Koushik Oct 5 at 7:35
  • 2
    $\begingroup$ I actually include myself among these "some people" (not for this particular tag which I don't subscribe, but many others). And also in congresses/seminars I attend which are supposedly in "my" field. This is part of student/researcher's life. If a subtopic is broad it's normal not to understand all its aspects, no shame. $\endgroup$ – YCor Oct 5 at 7:45
  • $\begingroup$ Yes, master.. no shame :) $\endgroup$ – Praphulla Koushik Oct 5 at 7:54
7
$\begingroup$

I don't think a new tag is necessary here. Usually, we want a new tag when a single term is used in quite different ways in different fields. Here, the concepts are essentially the same - in both topological and schematic settings, you can define vector bundles in terms of structure morphisms and the existence of a trivialization by open cover.

There may be some merit to revising the tag info.

$\endgroup$
  • $\begingroup$ I am thinking people who can comfortably think of vector bundles in the set up of manifolds has difficulty in seeing them in algebraic geometry... Am I misunderstanding? Just adding the term "over a scheme" might not make much difference.. $\endgroup$ – Praphulla Koushik Oct 4 at 2:43

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .