Stack algebraic geometry7/23/2023 ![]() Annales scientifiques de lcole Normale Suprieure 36.5 (2003): 747-791. ![]() \longrightarrow \mathcal^n$, and the above steps don't quite get me there. Logarithmic geometry and algebraic stacks. I've found that the best way to resolve things like this is to start googling, going to the library (though, uh, with the way the world is right now, this might need some adjustment), and asking people who know more than I do what's up.I want to get an intuition for the Euler sequence by understanding the explicit construction of maps between terms. This problem is not unique to algebraic geometry - in fact, in some ways, algebraic geometry has done a lot of work to get rid of this sort of thing via resources like Vakil's online notes and Stacks Project, though neither are full and complete references. It does happen sometimes in mathematics that there are things that "everybody knows" which can be pretty frustrating when you're not among the "everybody". Subjects: Algebraic Geometry (math.AG) Cite as: arXiv:math/9911199 math. The intuitive way to do this is to construct a square-root of the equation of the curve $C$, and this actually works: if our sextic is cut out by a homogeneous degree-six equation $f(x,y,z)$, then the equation $w^2=f(x,y,z)$ inside the weighted projective space $\Bbb P(1,1,1,3)$ with coordinates $x,y,z,w$ will cut out our ramified double cover.Īs for part 3, no, there's no conspiracy that I'm aware of. After introducing the general theory, we concentrate in the example of the moduli stack of vector budles, giving a detailed comparison with the moduli scheme obtained via geometric invariant theory. To construct $\pi$ explicitly, the idea is that one wants to emulate the construction of the square-root function as a double cover of the complex plane ramified at the origin. 1,227 7 7 silver badges 11 11 bronze badges endgroup 6. algebraic-geometry complex-geometry algebraic-curves Share. Artin, The implicit function theorem in algebraic geometry, Algebraic. Stack Exchange network consists of 182 Q
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