3

Is there a way to define a custom environment (for example Propositions) in such a way that the content of that environment will automatically have a given margin at the top and the bottom?

I mean something like

Margin to Proposition environment

Here's a MWE:

% Document etc (fold)
        \documentclass[]{article}
        \usepackage[utf8]{inputenc}
        \usepackage[T1]{fontenc}
        \usepackage{amssymb,amsmath}
        \usepackage{amsmath}
        \usepackage{amsthm}
        \usepackage{mathrsfs}

        \newtheorem{prop}{Proposition}[]
 \newcommand{\calO}{\mathscr{O}}
        \newcommand{\OX}{\calO_X}
 \newcommand{\OC}{\calO_C}
 \newcommand{\OD}{\calO(D)}
 \newcommand{\OXD}{\OX(D)}
 \newcommand{\ND}{\calN_D}
 \newcommand{\ODD}{\calO_D(D)}
 \newcommand{\Mtt}{\tilde{M}_t}  
 \newcommand{\Xdr}{X_d^r}  
 \newcommand{\Xdrr}{ X_d^{\underline{r}} }  
 \newcommand{\Wdr}{W_d^r}  
 \newcommand{\Wdrr}{W_d^{\underline{r}}}  
 \newcommand{\Gdr}{G_d^r}  
 \newcommand{\eps}{\varepsilon}
 \newcommand{\AND}{\qquad \text{and} \qquad}
 \DeclareMathOperator{\Pic}{Pic}
 \newcommand{\ABiff}{if and only if }
 \newcommand{\al}{\alpha}
 \newcommand{\alb}{{\alpha\beta}}
 \newcommand{\set}[1]{\Big\{ #1 \Big\}}


    \begin{document}

            With the aim of describing the tangent space of $\Wdr$, we will first look at the one of its canonical blow-up $\Gdr$. A motivation for this approach is the observation that the natural projection
    $$ \pi:\Gdr\to\Wdr, \qquad (L,W) \mapsto L $$
    is biregular away of $W_d^{r+1}$. Indeed $\pi$ is clearly a regular map and, further, the preimage of a $L\in \Wdrr$ consists just of the point $w=(L,H^0(L))$. It follows that, as far as $\Wdrr$ is regarded, $\pi_*$ gives an isomorphism between the tangent spaces
    \begin{equation}\label{eq:tgnt_Wdrr}
            T_{w}\Gdr \cong T_L\Wdr, \quad \forall L\in\Wdrr.
    \end{equation}
    In order to describe the tangent space of $\Gdr$, a preliminary result about the first order deformations of a pair $(L,s) \in \Pic^d \times H^0(L)$ will turn out to be crucial.
    \begin{prop}
            Let $L\in \Pic^d$ be a line bundle over $X$ and $s\in H^0(L)$ a global section. Then an element $\phi \in T_L\Pic^d \cong H^0(\OX)$ induces a first order deformation of the pair $(L,s)$ \ABiff $\phi\cdot s=0$ in $H^1(L)$.
    \end{prop}
    \begin{proof}
            Assume that $L$ is given by transition functions $g_\alb$ on a open cover $U_\al$ of $X$. We already know that $T_L \Pic^d \cong H^1(\OX)$ and a first order deformation $L'$ of $L$ is represented by a class $\phi \in H^1(\OX)$ in the following way
            $$ g_\alb \quad\overset{\phi}\leadsto\quad g'_\alb = g_\alb \cdot (1+ \eps \phi_\alb). $$  
            On the other hand, on a first order deformation of the pair $(L,s)$ into $(L',s')$ we have the additional requirement that the section $s'$ corresponds to a linear deformation of $s$. In formula this is expressed as
            $$ s'_\al = s_\al + \eps t_\al, \quad t \in H^0(L). $$
            The action of the transition functions can therefore be expanded as
            $$ s'_\beta = g'_\alb \cdot s'_\al \;\iff\; s_\beta + \eps t_\beta = g_\alb \cdot (1 + \eps \phi_\alb)\cdot(s_\al + \eps t_\al)$$
            and imposes the conditions
            $$ s_\beta = g_\alb \cdot s_\al \AND \phi_\alb \cdot s_\al = t_\al - g_{\beta\al}\cdot t_\beta. $$
            The first one is automatically satisfied since $s$ being a global section of $L$, while the second one can be rewritten in terms of the coboundary map $\delta : C^0(L) \to C^1(L)$ as
            $$ \phi \cdot s = \delta (t), $$
            thus giving the desired result.
    \end{proof}

    \end{document}
3

You should define your own theorem style via \newtheoremstyle:

enter image description here

\documentclass{article}
\usepackage{amsthm}% http://ctan.org/pkg/amsthm
\usepackage[nopar]{lipsum}% http://ctan.org/pkg/lipsum

\newtheoremstyle{spacytheorem}
  {2\baselineskip} % Space above
  {2\baselineskip} % Space below
  {} % Body font
  {} % Indent amount
  {\bfseries} % Theorem head font
  {.} % Punctuation after theorem head
  {.5em} % Space after theorem head
  {} % Theorem head spec (can be left empty, meaning `normal')
\theoremstyle{spacytheorem}
\newtheorem{prop}{Proposition}

\begin{document}

\lipsum[1]
\begin{prop}
\lipsum[2]
\end{prop}
\begin{proof}
\lipsum[3]
\end{proof}
\lipsum[4]

\end{document}

The settings for \newtheoremstyle is presented in the amsthm documentation (section 4.3 New theorem styles, p 4).

  • \lipsum does nasty things that force the qed box to a new line. someone actually using this should avoid \par before \end{proof}. – barbara beeton Mar 19 '15 at 20:37

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.