If I have two curves inside a projective surface, their intersection number should be the degree of their intersection product, i.e., I "move them" a bit so that they intersect properly and then consider the divisor consisting of their intersection points counted with the right multiplicity, and then add up those multiplicities. So far, is that right? I know this is a bit informal and I do not want formal answers based on formulas and computations, I just want an intuitive explanation: how is it possible that I ever get a negative number? Even more specifically, how can the multiplicity for the intersection of two curves at a point be negative? If they intersect properly, should the intersection number not just be 1 at every point, so that the total intersection number of the two curves is just the number of intersection points (which is clearly non-negative)?
Consider the blow-up of the plane in one point. Let $E$ the exceptional divisor. We know that $(E,E)=-1$. What is the geometrical reason for which the auto-intersection of $E$ is $-1$? In general, what does it mean, geometrically, that a divisor has a negative self-intersection or that the "right" number of divisors gives rise to a negative intersection?  Thanks.
How can I use QGIS to create a metro style map Why is "our today's meeting" wrong? One of the answers to  question states that &quot;We shall discuss it in our today's meeting&quot;  is grammatically correct. To me, that sentence is clearly wrong. While in today's meeting is fine and in our today meeting is OKish (though at the very least clumsy), there's something about the possessive there (our today's) that makes it wrong for me. I would read that sentence as in our today's (as opposed to your today's) meeting. Similar to in our car's trunk where the our clearly modifies car and not trunk or car trunk, the our in our today's seems to be modifying today's and not meeting. So, my questions are i) is it actually grammatically wrong to say in our today's or is it just a question of usage? and ii) if it is indeed wrong, how can we explain its wrongness? Citing @inbook with biblatex: how to put authors/editors before book title? Let $V$ be a subspace of $\mathbb R^3$ generated by the vectors $\{(1,1,1),(0,1,1)\}.$ There are $3$ vectors $u_1=(0,0,1),u_2=(1,1,0),u_3=(1,0,1)$.Then which of the following sets are connected?  $1.\left(\mathbb R^3\setminus V\right)\cup\{(0,0,0)\}$  $2.\left(\mathbb R^3\setminus V\right)\cup \{tu_1+(1-t)u_3:t\in [0,1]\}$  $3.\left(\mathbb R^3\setminus V\right)\cup\{tu_1+(1-t)u_2:t\in [0,1]\}.$  $4.\left(\mathbb R^3\setminus V\right)\cup \{(t,2t,2t):t\in \mathbb R\}$  Now $V$ is generated by two linearly independent vectors so is like $\mathbb R^2.$ So $\left(\mathbb R^3\setminus V\right)$ will be disconnected but giving the $(0,0,0)$ with them will make it connected.  No. $4$, I think will be connected also because $\{(t,2t,2t),t\in \mathbb R\}$ is in $V$ and contains the point $(0,0,0)$ Now, any neighbourhood of this point will have points from both $V$ and $\left(\mathbb R^3\setminus V\right)$ and so the union is connected.I'm not sure about no. $2$ and $3.$ In a modern SPFx Web Part, how do I check if a URL exists? Adding Labels and arrows in Tikz graph HTTP webpage is showing "Not Secure" in Chrome I've called GoDaddy a few different times and they said that it looks like it is a problem with my HTML file.  Except, my HTML file is the basic outline of a webpage, nothing fancy at all.    Chrome still says that the webpage is, "Not Secure" with the big red x over it.    I'm not sure what to do to fix it, I don't have any personal information on the site nor am I collecting any information from visitors (it's sort of an information site).  I shouldn't need an SSL certificate because I am not hosting anything privately. How can I convert monsters from D&D 3 or 3.5 to 2ed monsters? In case, if I get a multiple-entry Schengen visa in one of the embassies in Ukraine, Kyiv - should my first trip be to the country which issued the visa?  Any there any requirements of this sort? Does this condition vary depending on embassy which issued the visa?  What are the possible consequences on not visiting that country first? Does it somehow depend on country where the embassy is (i.e. non-Schengen and not EU members)? I am trying to create something similar to this in Tikz:    I have been looking at using the \shadedraw macro, but have not found a way to create the color spectrum.  It seems possible if I stack multiple gradient-shaded rectangles on top of each other, but I would rather not use such a lengthy and ugly solution.  Is there a way to recreate this PH-scale image in Tikz, ideally using few rectangles?  (Note: the number labels are not necessary, as they will be replaced with horizontal lines anyway.) (1, eval)('this') vs eval('this') in JavaScript? Like the title said, I want to install Celestia. I already downloaded the packages  and then, I tried all the things that I found on some posts (also, they're outdated, cause the last one is for Ubuntu 16.04) but nothing works.  How can I install it on Ubuntu 18.04.1? Time complexity of nested for-loop Reviewing suggested edit of own post after completing 20 reviews I've completed 20 suggested edits reviews today. Then, I came across a  and I approved it.   Then, I had a doubt that whether the review count has incremented or not, oh! it's not incrementing. System works fine.  But, take a look at review page,     The edit was already reviewed by one reviewer and then I reviewed it. As I'm the Owner of the post it's enough to approve the edit. But, the review history doesn't show the detail that I had approved it. It's misleading that only one vote of a reviewer who is neither the community user nor the OP nor the moderator, is enough.  So, what should we do in this type of situation?  Is it correct to make OP to review the suggested edit after completing daily limit?  Should we need to display/hide the OP has approved the edit in the review history? "It is not possible to check out a single file. The finest level of checkouts you can do is at the directory level."  How do I get around this issue when using Subversion?  We have this folder in Subversion where we keep all our images. I just want to check out one file (image) from that. This folder is really big and has ton of other stuff which I don't need now. For me the distinction between sites is purely topical. I get that there's a right and a wrong place to ask questions, but I regularly ask questions across a number of sites. They all log me in (in a weird sort of way), and now there's the global inbox.  I've read that there's a feed  and that there's a  but neither of these are what I want.  What I'd like is to have an RSS feed from my global inbox, i.e. to include notification of updates to my public questions, answers, comments. Is this possible? I tried this:  find . -type f -size 128 -exec mv {} new_dir/  \;   Which didn't work, and it didn't give me an error. Here is an example of what the file looks like, when using stat -x  $ stat -x ./testfile | grep Size    Size: 128          FileType: Regular File Windows 10 update broke my MBR / GRUB PHP function overloading I installed CCSM to enable window previews in Unity. But when I went into extras, there was no 'window preview' option.  So I tried experimenting with other options in Compiz and now there are no borders in the dialogue boxes (close, minimize, restore buttons are not there, I had enabled some 'flat....' option in Compiz.  Later, I uninstalled Compiz and then reinstalled it. Now it says      "Failed to load session Ubuntu"   I can't even access through the guest account, I am new to Ubuntu.(please explain in detail).  All I have access to is the login screen (it still shows my custom wallpaper). Please help, I don't want to lose my stuff.