All Questions
Tagged with curves ag.algebraic-geometry
10 questions with no upvoted or accepted answers
5
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0
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413
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Most divisors on a curve aren't special?
I have a generic smooth curve $C$ of genus $g$ and fixed multiplicities $a_1, \dots, a_n \geq 0$ with $\sum a_i = g+1$.
Q1 : For generic marked points $p_1, \dots, p_n \in C$, must $\sum a_i p_i$ be a ...
5
votes
0
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333
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Which equation of a Butterfly?
Let $A, B$ be two points and $L$ be a line on the Euclidean Plane. Take two points $J, G$ on the line $L$ such that $JG=constant$. Let $AJ$ meet $BG$ at $P$, $AG$ meet $BJ$ at $Q$, then the locus of ...
4
votes
0
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145
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How many times do I have to blow up such a curve until it is smooth?
If I have parametrized a curve in the complex plane by $$x(t)=a_lt^l+\cdots+a_nt^n$$
$$y(t)=b_kt^k+\cdots+b_mt^m$$
and the image is reduced (there exist at least two exponents which are relatively ...
3
votes
0
answers
303
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An algebraic proof: A line bundle on a curve with a connection must be of degree 0
Let me state it using the language of $D$-modules. Let $X$ be a smooth projective curve and $\mathcal{L}$ a line bundle on it. Assume that $\mathcal{L}$ has a left action of $\mathcal{D}_X$. Then show ...
3
votes
0
answers
160
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Semistability of restrictions of a semistable vector bundle over a reducible nodal curve
Let $C$ be a reducible nodal curve over complex numbers with two smooth components $C_1$ and $C_2$ intersecting at the only node $P$. Let $E$ be a $\omega$ semistable vector bundle over $C$ of rank $r$...
3
votes
0
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118
views
How order of divisor with support at infinity is changed at reduction?
Jing Yu in his paper "On Arithmetic Of Hyperelliptic Curves" on page 5 asserts the following
The most interesting case is certainly the case $k = \mathbb Q$ and $D \in \mathbb Z[t]$.
To decide ...
1
vote
0
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115
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Cokernel of map of dual of sheaves of differentials/deformations
Let $C$ be a nodal projective curve over an algebraically closed field of genus at least $2$. There are two natural "differential objects" one can consider: The sheaf of differentials $\...
1
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0
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119
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More on points on a curve of genus 3
Let $Y$ be a smooth complex projective curve of genus two,
$X$ a Galois cover of degree two of $Y$ and $K$ the canonical
divisor of $X$. Let $i$ be the involution of $X$ over $Y$.
Can one find two ...
1
vote
0
answers
239
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Proposition from Kollar's Rational Curves on Algebraic Varieties
$\DeclareMathOperator\Hom{Hom}$I have some questions on a proof of Proposition II.3.10 & notations from Rational Curves
on Algebraic Varieties by Janos Kollar (page 117).
We work in setting ...
1
vote
0
answers
516
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support of embedded points in a curve
Let $C \subset \mathbb{P}^n$ be an one dimensional scheme. Suppose that $C$ decomposes as the union of a Cohen Macaulay reduced curve $\tilde{C}$ (in particular $\tilde{C}$ does not have embedded ...