![]() ![]() Most of those topics are actually not discussed in introductory texts. To actually find interesting examples knowledge of toric varieties is helpful. While the theory of schemes proved to be useful to describe a wide class of phenomena in. For example model building in $F$-theory requires among other things to the study of singularities of elliptic fibrations and the approximate dynamics of certain branes is determined by variations of hodge structure. An algebraic stack is a generalisation of the concept of scheme. The sections on algebraic geometry in 'Mirror Symmetry' (Clay/AMS) are essentially a Crib Notes version of that paper and some of the classic CY and special geometry papers referred to above. Especially 14 and 15 should be interesting to you, even if you did not take a course in string theory yet.īy now there are of course a lot of other applications of ideas from algebraic geometry to the study of string theory beyond those ordinarily found in textbooks. Griffiths and Harris 'Principles of Algebraic Geometry' (Wiley) is the best for your purposes (read only the parts on Kahler geometry). Just to get an idea what ideas were needed in string theory 25 years ago a look at chapter 12,14,15,16 in the second volume of Green, Schwarz, Witten might be helpful. Griffiths and Harris is very good, but probably not suitable as your only source for self-study. Audun Holme has taken up Euclid’s challenge as well, and written a new book A Royal Road To Algebraic Geometry recently published. In mathematics, in particular algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects. While this story may or may not be apocryphal, Euclid’s pithy response has lent its name to any number of books and articles over the years. SciPy provides algorithms for optimization, integration, interpolation, eigenvalue problems, algebraic equations, differential equations. We will discuss a functorial approach to algebraic geometry, leading to the ubiquitous theory of algebraic stacks. I am not sure, if they are available online. Euclid replied simply that There is no royal road to geometry. They are written with string theory in mind and cover a lot of basic ground. One good source my undergraduate adviser recommended to me are the lecture notes of Candelas on Complex Geometry. algebraic-geometry algebraic-curves surfaces schemes divisors-algebraic-geometry. The texts I have found so far are all rather dry and almost completely lack this informal streak, and all of them are geared towards pure mathematicians, so if there exists something like "Algebraic geometry for physicists" and "Kahler manifolds for physicists" (of course, they would probably have different titles :)), I would greatly appreciate the relevant references. Stack Exchange network consists of 182 Q
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