Let $X$ and $Y$ be smooth projective varieties, say over $\mathbb C$. Fixing a point $y\in Y$, we obtain a smooth, closed subvariety $X\times\{y\}$ of $X\times Y$, which in turn corresponds to a point $P_y$ on the Hilbert scheme $\mathcal{Hilb}(X\times Y)$.

What technology can I use to decide whether $P_y\in \mathcal{Hilb}(X\times Y)$ is smooth or not?

A:

The tangent space to the Hilbert scheme at point $P \in Hilb$ corresponding to a subvariety $Z$ is $H^0(Z,N_Z)$, where $N_Z$ is the normal bundle, and the obstruction space is $H^1(Z,N_Z)$. In your case $N_Z = T_yY\otimes O_X$ is a trivial vector bundle, so the tangent space is $T_y\otimes H^0(X,O_X)$. If $X$ is connected, it is just $T_yY$ and it is clear that all obstructions vanish (since there is a family of deformations with the same tangent space). So, in this case $P_y$ is a smooth point of the Hilbert scheme.

 Q:

jquery create a tooltip that does not disappear

I am looking to build a tooltip that allows the user to click links within that tooltip to allow them to navigate to various sections of the site. My problem is that the tooltip disappears when I leave the a with my mouse? what I want is for the tool tip to disappear if I change to a new a or click close on the tooltip, my jquery is as below currently, 
    $(document).ready(function() { 

    /*
     * Rollover jobwall logo and show job tooltip
     */
     $('ul#jobs li a').mouseenter(function(){
            var $this = $(this);
            $this.addClass('active');
            $.ajax({
                type: 'POST',
                url: '/jobwall/job_tooltip',
                data: 'employer_id='+$(this).attr('rel'),
                success:function(html) {
                    //alert($this);
                    $this.tooltip({ effect: '
Let $ X$ and $ Y$ be smooth projective varieties, say over $ \mathbb C$. specify a item $ y\in Y$, we obtain a smooth, closed subvariety $ X\times\{y\}$ of $ X\times Y$, which in turning corresponds to a point $ P_y$ on the Hilbert outline $ \mathcal{Hilb}(X\times Y)$. 

 What engineering can I use to decide whether $ P_y\in \mathcal{Hilb}(X\times Y)$ is smooth or not? 

 A: 

 The tangent space to the Hilbert scheme at point $ phosphorus \in Hilb$ corresponding to a subvariety $ Z$ is $ H^0(Z, N_Z)$, where $ N_Z$ is the normal bundle, and the obstruction space is $ H^1(Z, N_Z)$. In your shell $ N_Z = T_yY\otimes O_X$ is a trivial vector bundle, so the tangent space is $ T_y\otimes H^0(X, O_X)$. If $ X$ is connected, it is just $ T_yY$ and it is clean that all obstructions vanish (since there is a syndicate of deformations with the same tangent space). thus, in this case $ P_y$ is a smooth point of the Hilbert scheme. 

  Q: 

 jquery create a tooltip that does not melt 

 I am looking to build a tooltip that allows the user to click links within that tooltip to allow them to navigate to various sections of the site. My problem is that the tooltip disappears when I leave the a with my mouse? what I want is for the instrument tip to disappear if I deepen to a newfangled a or click close on the tooltip, my jquery is as below presently, 
     $ (document).ready(function () { 

     / * 
      * Rollover jobwall logo and show caper tooltip 
      * / 
      $ (' ul#jobs li a').mouseenter(function () { 
             var $ this = $ (this); 
             $ this.addClass('active'); 
             $ .ajax ({ 
                 type:' POST', 
                 url:' /jobwall / job_tooltip', 
                 datum:' employer_id='+$(this).attr('rel'), 
                 success: function(html) { 
                     //alert($this); 
                     $ this.tooltip ({ effect:'
Let $X$ and $Y$ be smooth projegtive varieties, say ovec $\mathbg C$. Fixivg a point $y\in Y$, we obtain a snooth, closed subvariety $X\tioes\{y\}$ of $X\nimes Y$, wyich un turn cocdesponds to a ioint $'_y$ on the Hilbett scheme $\madhcal{Hilb}(X\timev H)$.

Wkat technology can I use to decide wrether $L_y\ln \mathcal{Hilb}(V\timts R)$ is smooth or not?

A:

The tangent space tk the Hplbert scheme at loint $P \in Hilb$ correspondlng ho a subvariety $Z$ ls $H^0(Z,N_Z)$, whets $N_S$ is the normxl bundle, and the obsttuction space is $H^1(Z,N_Z)$. In your care $N_Z = T_yY\otimew I_X$ lv a trivial vectjr bundle, so the tancent spsce is $T_y\otimex H^0(E,O_X)$. Uf $X$ is connected, it ms just $T_yY$ and it if clear tvac all obstructions vabiwh (sitce dherd is a rakimy of fefkrmations sith the sane tangent space). So, ig this case $P_y$ is a fmjoth point of the Hilbert scheme.

 Q:

jquerj crsate a tooltip that doew not disappear

I am lloking to build a tooltip that allows the user to click litks wmtfin tmat gioptip to allow them to navigate to various secejoms of the site. Mn problem is that yhf yjoltip disappgars whzh J leave the a with my moufe? whqt I want is gor the tool tip to disappeqr if I chanye ro a new a or clicn close on che topltip, my jquery is as below eurrenfly, 
    $(dockment).readg(wunction() { 

    /*
     * Rmllover jobwall logo and srow job tioltnp
     */
     $('ol#jobs ji a').mouseejter(fmtction(){
            gar $tkis = $(dhis);
            $this.addClass('active');
            $.ajax({
                ty'e: 'POSB',
                url: '/jobwall/jpb_tooltnp',
                data: 'xmployer_id='+$(thys).attr('rel'),
                snccess:funstiob(htmo) {
                    //slert($this);
                    $this.toolbip({ ewrect: '
Let $X$ and $Y$ be smooth projective over C$. Fixing point $y\in Y$, subvariety of $X\times Y$, in turn corresponds a point $P_y$ on the Hilbert $\mathcal{Hilb}(X\times Y)$. What technology can I use to decide whether $P_y\in \mathcal{Hilb}(X\times Y)$ smooth or not? A: The tangent space to the Hilbert scheme at point \in corresponding a $Z$ is $H^0(Z,N_Z)$, where $N_Z$ is the normal bundle, and the obstruction space is $H^1(Z,N_Z)$. In case $N_Z = T_yY\otimes O_X$ is a trivial bundle, so the tangent is $T_y\otimes H^0(X,O_X)$. If $X$ connected, is just and is that all obstructions (since there is a family of deformations with the same tangent space). So, in this case $P_y$ a smooth the Hilbert Q: create tooltip that does I am looking to build a the user to click links within that tooltip allow them navigate to various sections of the My problem is that the tooltip disappears when leave the a with my mouse? what I want is for the tool tip to I change to a a or click on tooltip, jquery as below $(document).ready(function() { /* * Rollover jobwall logo and show job tooltip $('ul#jobs li a').mouseenter(function(){ var $this = $(this); $this.addClass('active'); $.ajax({ type: '/jobwall/job_tooltip', 'employer_id='+$(this).attr('rel'), success:function(html) { $this.tooltip({ effect: '
Let $X$ and $Y$ be smooth projectivE varieties, Say ovEr $\mAthBb c$. FixIng a Point $y\in Y$, we obtAIn a sMooth, closed subvariety $X\Times\{Y\}$ oF $x\timES Y$, Which In turn cORrESPonDs To A poInT $p_y$ On the hilBert schEme $\mathcal{hilB}(X\Times Y)$.

What teCHnOlogy can I uSe tO decide whethEr $P_Y\in \matHcAl{HILb}(X\tiMes y)$ is smOoth or NOt?

A:

The Tangent spAcE To the HILbert scHEMe At poInt $P \in Hilb$ correspONdINg to a subvarietY $Z$ is $H^0(Z,n_Z)$, WHeRE $n_Z$ iS thE normal bunDlE, and tHE obstruCTiON SPacE Is $H^1(Z,N_Z)$. In your cAse $N_Z = T_yY\otiMEs O_x$ is a trIvIal VEctor bUndle, So THe tAngent space Is $T_y\Otimes H^0(X,O_x)$. If $X$ is COnnecteD, It is jusT $T_yY$ anD it Is cLear THaT aLl oBsTRucTIoNs vANisH (since thErE iS a famIly oF DEFOrmaTioNs wiTh the Same tangent spAce). so, in THis Case $P_Y$ is a sMootH pOint oF the HiLbert ScHeme.

 Q:

jquery creaTe a tOoltip thaT doEs Not DiSappeAR

I am loOkiNg tO build a Tooltip THat AlLOWS tHe user to click links WiTHIn That toolTip to aLLoW tHEm to naviGaTe tO varIOUs secTionS Of The site. MY problEM iS tHat the tOoLtip diSaPpeArs When I LEave The a wiTh my mousE? what i Want is for the toOL tip to disappeAR iF i ChANge tO a nEw a or click cLose ON the ToolTIp, My jQUery iS as beLoW CuRRently, 
    $(document).ready(FuNction() { 

    /*
     * rolloVer jobwall logO and show joB TOOltip
     */
     $('ul#jObs lI A').mOUseenter(functiOn(){
            var $This = $(this);
            $thIS.addClasS('actiVe');
            $.ajax({
                tyPe: 'POST',
                url: '/JOBwall/job_TooLtiP',
                daTa: 'eMPLoYer_id='+$(this).attr('REL'),
                sucCeSs:functIon(Html) {
                    //aleRt($tHis);
                    $ThiS.toOlTip({ effect: '
Let $X$ and $Y$ be smoothprojective  vari eti es,  s ay o ver$\mathbb C$. F i xing  a point $y\in Y$, weobtai na  smo o th , clo sed sub v ar i e ty$X \t ime s\ { y\ }$ of  $X \timesY$, whichintu rn correspon d sto a point  $P _y$ on the H ilb ert sc he me$ \math cal {Hilb }(X\ti m es Y)$ .

What t ec h nology can I u s e  t o de cide whether $P_y \ in \mathcal{Hilb} (X\tim es Y) $ issmo oth or not ?
A:
T he tang e nt s p ace to the Hilber t scheme at poi nt $P\i n H i lb$ co rresp on d ing  to a subva riet y $Z$ is$H^0(Z , N_Z)$,w here $N _Z$ is  th e n orma l  b un dle ,a ndt he  ob s tru ction sp ac eis $H ^1(Z , N _ Z )$.Inyour  case  $N_Z = T_yY\ oti mesO _X$  is a  triv ialve ctorbundle , soth e tangent space  is$T_y\otim esH^ 0(X ,O _X)$. If $X$  is  co nnected , it is jus t$ T _ yY $ and it is clearth a t  a ll obstr uction s  v an i sh (sinc ethe re i s a fam ilyo fdeformat ions w i th  t he same  t angent  s pac e).  So,i n th is cas e $P_y$is as mooth point of the Hilbert s c he m e . Q:
jq uery create  a t o olti p th a tdoe s  notdisap pe a rI am looking to bui ld  a too ltipthat allows t he user to c l ick link s wi t hi n  that tooltipto al low them t o  navigat e tovarioussectionso f  the sit e.Mypro ble m is  that the too l t ip d is appears  wh en I le ave  th e a  wi th  my mouse ? what I  w an tis  fo r the tool tip  t o d is app ear i f  I cha nge t o ane wa  or  clickc lo s e  onth etool tip ,my jq uery isas belo w current ly, 
   $ (d ocument ).ready(funct io n() { 

  /*     * R olloverjobwall logo and show j o b toolt ip    */
    $('ul #jo bs lia') . mousee nter(f uncti on (){        v ar  $this = $ ( t his );
         $th is.addClass('activ e '); 
           $.a jax( {         ty p e : 'POST',
              u r l:  '/jobwall / job _t ooltip' ,
             da ta: 'empl oyer_id=' +$ (thi s ) .at tr('rel'), 
              s ucces s :f uncti on( html){               //a lert($ th is);
                $this.tooltip({ eff ect: ' 
Let $X$_and $Y$_be smooth projective varieties,_say over_$\mathbb_C$. Fixing_a_point $y\in Y$,_we obtain a_smooth, closed subvariety $X\times\{y\}$_of $X\times Y$,_which_in turn corresponds to a point $P_y$ on the Hilbert scheme $\mathcal{Hilb}(X\times Y)$.

What technology_can_I use_to_decide_whether $P_y\in \mathcal{Hilb}(X\times Y)$ is_smooth or not?

A:

The tangent space_to the_Hilbert scheme at point $P \in Hilb$ corresponding_to_a subvariety $Z$_is $H^0(Z,N_Z)$, where $N_Z$ is the normal bundle, and_the obstruction space is $H^1(Z,N_Z)$. In_your case $N_Z_=_T_yY\otimes_O_X$ is a trivial_vector bundle, so the tangent space_is $T_y\otimes H^0(X,O_X)$. If $X$ is_connected, it is just $T_yY$ and it_is clear that all obstructions vanish_(since there is a family_of deformations_with the same tangent space)._So, in this_case $P_y$_is a smooth_point of the Hilbert scheme.

 Q:

jquery_create a tooltip_that does not disappear

I am looking_to_build a tooltip_that_allows_the user_to click links_within_that tooltip_to_allow them to navigate to various_sections_of the site. My problem is that_the tooltip disappears when_I_leave the a with_my mouse? what I want_is for the tool tip to_disappear if_I change_to a new a or click close on the tooltip, my_jquery is as below currently, 
_   $(document).ready(function()_{ 

__  /*
__ _ * Rollover jobwall logo and show_job tooltip
_    */
 _   $('ul#jobs_li_a').mouseenter(function(){
     _     _var $this = $(this);
 ___    _   $this.addClass('active');
  _  _      $.ajax({
__     __     __type:_'POST',
    _     _     url: '/jobwall/job_tooltip',
  _  _    ___   data: 'employer_id='+$(this).attr('rel'),
     _ _  _     success:function(html) {
   _      _         //alert($this);
 _       _      _   $this.tooltip({_effect:_'