9 votes

What relationship is there between repeated roots of discriminants and orders of roots of the original polynomials?

(1) There is the following indirect explanation: For a generic curve neither of these phenomena happen - the discriminant has no repeated roots and the branch points all have ramification index two. ...
Will Sawin's user avatar
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9 votes
Accepted

What relationship is there between repeated roots of discriminants and orders of roots of the original polynomials?

$\def\P{{\mathbb{P}}} \def\A{{\mathbb{A}}} \newcommand{\O}{\mathcal{O}} \DeclareMathOperator{\Disc}{Disc}$I think the story goes like this. The multiplicity of a zero of the discriminant counts ...
Jack Huizenga's user avatar
4 votes

Intersection complex of genus-zero curves?

Not a complete answer, too long for a comment. I think you'd find it useful to think about these things in terms of Hassett's moduli spaces of weighted pointed curves. Here's the brief version. Fix a ...
Dan Petersen's user avatar
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3 votes
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Lifting of quadrics containing a curve

1-normality is sufficient, i.e. it suffices that $H^0(\mathbb P^r, \mathcal O_{\mathbb P^r}(1))\to H^0(C, \mathcal O_C(1))$ is surjective. Indeed, choose class $q \in H^0(\mathbb P^r, \mathcal O_{\...
Will Sawin's user avatar
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2 votes

Motivation for zeta function of an algebraic variety

Here's the simple motivation going back to the beginning with Riemann of the cottage industry of zeta functions. The Euler product for the Riemann zeta function is $$\zeta(s) = \prod_p \frac{1}{1-p^{-...
Tom Copeland's user avatar
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