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Results tagged with ag.algebraic-geometry
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user 69320
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
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polynomials with similar maxima-minima
Assume $p$ and $q$ are n-variate degree d, homogeneous polynomials. Define $ |p|_{\infty}= \max_{x \in S^{n-1}} |p(x)|$
$D(p)=\{ x \in S^{n-1} : p(x)= |p|_{\infty} \}$
$E(p)=\{x \in S^{n-1} : p(x)= - …
- 351
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Counting Zeros Under Unitary Action
Assume we have two polynomials $f_1$ and $f_2$ with Newton polytopes $A_1 , A_2 \in \mathbb{Z}^2$. Also suppose that coefficients of $f_1$ and $f_2$ are generic. Then we pick a unitary matrix $Q$ and …
- 351
3
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Average nastiness of a Newton polytope
Given a Newton polytope $P$ inside the $d$-scaled simplex ( i.e $\alpha \in P \implies | \alpha |=d $ ), then we define the following quantity:
$$ P(x)= \left( \sum_{\alpha \in P} \binom{d}{\alpha …
- 351
4
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What is the interface between functional analysis and algebraic geometry?
I do not know if this is what you are looking for but I heard people speaking of Banach Algebraic Geometry. I can also note the fascinating work of Semyon Alesker (using algebra-geometric tools on say …
- 351