# Tagged Questions

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### Conceptual algebraic proof that Grassmannian is closed in Plucker embedding

I'm planning lectures for my intro algebraic geometry course, and I noted something awkward that is coming up. We're starting projective varieties soon. Of course, we'll prove that projective maps are ...
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### Easy to state applications of dimension theory in algebraic geometry

Dimension theory is quite a sophisticated topic (at least for me), it is fully settled in Shafarevich's book on the first 100 pages. Shafarevich gives two nice applications of the theory. 1) A proof ...
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### Higher dimensional Bezout via Hilbert polynomials: a reference

For the purposes of teaching my elementary course in algebraic geometry I am looking for a reference (or notes) that contains a complete proof of a higher-dimensional weak Bezout theorem. I only want ...
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### “Classical” consequences of Bezout's theorem in dimensions $>2$

By Classical I mean something that could have been found before 1900 (say). A well known consequence of Bezout's theorem for plane curves is Pascal's theorem ...
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### Lines on degree 2n-3 Fermat hypersufaces

It is well known that a generic hypersurface of degree $2n-3$ in $\mathbb CP^n$ has finite number of lines. I would like to ask a couple of questions about lines on Fermat hypersurfaces and their ...
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### Pedagogical notes on line bundles on complex projective manifolds

I would like to find some notes (or book), that explains on a very basic level what is a line bundle on a complex projective manifold. Maybe even, what is a line bundle on $\mathbb CP^n$. It seems ...
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### Explaining the concept of projective space: notes for students

This is a question on teaching. I am teaching at this moment a course in algebraic geometry for master students on a very basic level. Today (this was the fourth lecture) I discovered that only four ...
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### Varieties as an introduction to algebraic geometry / How do professional algebraic geometers think about varieties

This really is two questions, but they are kind of related so I would like to ask them at the same time. Question 1: In a question asked by Amitesh Datta, BCnrd commented that it is important to ...
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### The etale fundamental group of a field

Background and motivation: I am teaching the "covering space" section in an introductory algebraic topology course. I thought that, in the last five minutes of my last lecture, I might briefly sketch ...