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Jul
24
awarded  Popular Question
Jul
20
revised Interesting facts and problems to motivate high school combinatorics students
edited tags
Jul
20
asked Interesting facts and problems to motivate high school combinatorics students
Jul
16
comment Is every Hausdorff space metric?
@Berci which means Hausdorff, no?
Jul
16
asked Is every Hausdorff space metric?
Jul
11
comment linear systems and maps
I think now it's clearer, thank you. The only thing seems confused to me is where is the linear system given. We have to take an arbitrary linear system and get a map associated to this linear system. If I followed your answer you begun with a variety (instead of a linear system) and get a map. Thank you again!
Jul
11
comment linear systems and maps
Thank you for your answer. what is a section and a line bundle? my definition of linear system is the same as Fulton's one, i.e., let $D$ be a divisor over a curve and $V$ be a vectorial subspace of $L(D)$. The set of divisors $\{div(f)+D|f\in V\}$ is called a linear system associated to $V$. If $V=L(D)$, then the linear system is called complete and we denote by $|D|$.
Jul
11
comment linear systems and maps
@Relapsarian do you know another book which explain this concept in a more basic way?
Jul
10
comment linear systems and maps
@Relapsarian My only background is Fulton's Algebraic Geometry book. I don't know about schemes. Thanks.
Jul
10
comment Example of a curve with this property
I didn't study about ramidied coverings yet. I'm trying this construction: Given a regular map $\varphi:C\to \mathbb P^n,P\mapsto \mathbb (f_0(P):f_1(P):\ldots:f_n(P))$, we can associate a linear system $|\varphi|$ in the following manner: let the divisor $D=-\min div(f_i)$ and $V$ be the vector space of every linear combination of the functions $f_i$. Thus we define $|\varphi|=\{div(g)+D\mid g\in V\}$. If $\varphi:C\to \mathbb P^1$, where $\varphi=(f_1,f_2)$ and $f_1=y/x$ and $f_2=x^2/y^2$, then $D=P_1+2P_2$ and $\deg(D)=3$. So this $C$ is a trigonal curve, right?
Jul
10
asked linear systems and maps
Jul
10
asked Example of a curve with this property
Jul
10
revised Definition of trigonal curves
added 69 characters in body
Jul
10
comment Definition of trigonal curves
@Relapsarian I'm sorry, I meant "So Can I say that a curve C is trigonal if it has a divisor which has a linear system $g_3^1$?" See the last line of my question again please.
Jun
22
comment Definition of trigonal curves
This map $C\to \mathbb P^1$ you mentioned is not necessarily a canonical embedding, right?
Jun
21
revised Books to help us to draw 3D pictures
added 154 characters in body
Jun
21
comment Books to help us to draw 3D pictures
@copper.hat I'm looking for sites or books which teach how to draw them. I saw some mathematicians which can draw difficult pictures as möbius band very well. I thought maybe they learn from somewhere.
Jun
21
comment Books to help us to draw 3D pictures
@JasperLoy yes, as I said above.
Jun
21
comment Books to help us to draw 3D pictures
@copper.hat no, you didn't follow my question. I would like to draw these pictures myself in order to draw them on blackboard.
Jun
21
asked Books to help us to draw 3D pictures