# Tagged Questions

114 views

### How to imagine “tensoring with Serre's twisted sheaf”

What has an algebraic geometer in mind when (s)he sees $\otimes \mathcal{O}(1)$? I think it has something to do with an intersection of a hypersurface...? Thanks, Adrian
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### What is a complete intersection?

I was reading and I encountered something that goes: We have degree $d$ polynomials in $s$ variables $F_1, ..., F_n$ with coefficients in integers. Let $X$ be the complete intersection defined by the ...
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### Degree of a divisor for algebraically closed fields vs not closed ones

Suppose we have an algebraically closed field $F$ and we consider the projective space $\mathbb{P}^1$ over $F$. If we consider some divisor $D = n_P P + n_Q Q +n_s S$, then we say the degree of $D$ ...
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### When is a series expansion related to its derivative by a polynomial equation?

Is there some common theory behind the following two examples? Example 1. Let $p(t) = \sum_{n \geq 0} (-1)^k t^{2k}/(2k)!$, and $x = p(t), y = p'(t)$. Then $x^2 + y^2 = 1$ identically. Example 2. ...
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