Skip to main content

All Questions

10 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
5 votes
0 answers
413 views

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 ...
Leo Herr's user avatar
  • 1,084
5 votes
0 answers
333 views

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 ...
Cố Gắng Lên's user avatar
4 votes
0 answers
145 views

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 ...
Taylor's user avatar
  • 251
3 votes
0 answers
303 views

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 ...
XT Chen's user avatar
  • 1,168
3 votes
0 answers
160 views

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 $r$...
Babai's user avatar
  • 290
3 votes
0 answers
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 ...
Maxim's user avatar
  • 424
1 vote
0 answers
115 views

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 $\...
Matthias's user avatar
  • 223
1 vote
0 answers
119 views

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 ...
user95246's user avatar
  • 237
1 vote
0 answers
239 views

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 ...
user267839's user avatar
  • 6,018
1 vote
0 answers
516 views

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 ...
NotNow's user avatar
  • 103