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P^1 -> ℙ¹ in title; `\text` and `\operatorname`
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LSpice
LSpice
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Moduli of parabolic bundles of rank two on P^1ℙ¹

IamI am trying to understand the structure of Moduli space of rank two parabolic bundles on $\mathbb{P}^1$, of degree zero or degree one, with weights $(\frac{1}{2},\frac{1}{2},...\frac{1}{2})$$(\frac{1}{2},\frac{1}{2},\dotsc\frac{1}{2})$ at $n$ points, say $n$ is even. For very small weights, the moduli space is a GIT quotient $((\mathbb{P}^1)^n)^{ss}/SL_2$$((\mathbb{P}^1)^n)^\text{ss}/SL_2$, by a paper of Moon-YooMoon–Yoo. Can the above half weight-case be written as an explicit blow-up  , blow-down of the quotient $((\mathbb{P}^1)^n)^{ss}/SL_2$.$((\mathbb{P}^1)^n)^\text{ss}/\operatorname{SL}_2$?

Moduli of parabolic bundles of rank two on P^1

Iam trying to understand the structure of Moduli space of rank two parabolic bundles on $\mathbb{P}^1$, of degree zero or degree one, with weights $(\frac{1}{2},\frac{1}{2},...\frac{1}{2})$ at $n$ points, say $n$ is even. For very small weights, the moduli space is a GIT quotient $((\mathbb{P}^1)^n)^{ss}/SL_2$, by a paper of Moon-Yoo. Can the above half weight-case be written as an explicit blow-up  , blow-down of the quotient $((\mathbb{P}^1)^n)^{ss}/SL_2$.

Moduli of parabolic bundles of rank two on ℙ¹

I am trying to understand the structure of Moduli space of rank two parabolic bundles on $\mathbb{P}^1$, of degree zero or degree one, with weights $(\frac{1}{2},\frac{1}{2},\dotsc\frac{1}{2})$ at $n$ points, say $n$ is even. For very small weights, the moduli space is a GIT quotient $((\mathbb{P}^1)^n)^\text{ss}/SL_2$, by a paper of Moon–Yoo. Can the above half weight-case be written as an explicit blow-up, blow-down of the quotient $((\mathbb{P}^1)^n)^\text{ss}/\operatorname{SL}_2$?

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john
john
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Moduli of parabolic bundles of rank two on P^1

Iam trying to understand the structure of Moduli space of rank two parabolic bundles on $\mathbb{P}^1$, of degree zero or degree one, with weights $(\frac{1}{2},\frac{1}{2},...\frac{1}{2})$ at $n$ points, say $n$ is even. For very small weights, the moduli space is a GIT quotient $((\mathbb{P}^1)^n)^{ss}/SL_2$, by a paper of Moon-Yoo. Can the above half weight-case be written as an explicit blow-up , blow-down of the quotient $((\mathbb{P}^1)^n)^{ss}/SL_2$.