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Questions tagged [algebraic-geometry]

Use for questions about algebraic geometry as it applies to physics. Purely mathematical questions should NOT go here, instead, they belong on Math Stack Exchange.

Algebraic geometry is fundamentally the study of geometric manifestations of solutions to systems of polynomial equations. This field is connected with such fields as complex analysis, number theory, and topology. It is used in physics in multiple fields, including string theory.

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Crash course on algebraic geometry with view to applications in physics

Could you please recommend any good texts on algebraic geometry (just over the complex numbers rather than arbitrary fields) and on complex geometry including Kahler manifolds that could serve as an informal introduction to the subject for a…
anonymous
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TQFTs and Feynman motives

Questions Is a topological quantum field theory metrizable? Or else a TQFT coming from a subfactor? For a given metric, are there always renormalization and Feynman diagrams? Is there always a Feynman motive related to the theory? Finally, does this…
Sebastien Palcoux
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Equation of a torus

In the recent paper http://arxiv.org/abs/1509.03612, page 37. They say that a torus can be described by the equation $$y^2=x(z-x)(1-x)$$ where $x$ is a coordinate on the base $\mathbb{P}_1$. Could someone explain why the torus is described by this…
Nahc
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What is Motivic mathematics and how is it used in physics?

In a few videos I've seen where he discusses the new approach to calculating the super Yang Mills scattering amplitudes, Nima Arkani-Hamed sometimes alludes to the use of Motivic methods as being relevant. (For example in the last few seconds of…
twistor59
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How algebraic geometry and motives appears in physics?

First, I'm not a physicist so I have just a little background in physics. I have been reading some noncommutative geometry books and papers (Connes, Rosenberg, Kontsevich etc) and a lot of high machinery from algebraic geometry such as étale…
user40276
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Relation between Topological String Theory and Physical String Theory?

I'm familiar with topological string theory from the mathematical perspective. In my narrow world, the topological string partition function is given by the Gromov-Witten partition function, which is equivalent to the Donaldson-Thomas partition…
Benighted
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How can I understand instantons as sheaves?

In specific, instantons are considered or interpeted as torsion free coherent sheaves. Why is that the case? Is there a nice way to understand this relation and of course also understand how the two moduli spaces (instantons and torsion free…
Marion
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Metric transformation, polygons and gravitons

I'm trying to understand the paper by Hitchin called: ''Polygons and gravitons". I'm stuck at page 471. At this point, he does some computations and obtains a metric: $$ \gamma dz d\bar{z}+\gamma^{-1}\left(\dfrac{2dy}{y}+\bar{\delta}dz…
user1201349
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Etale bundles and sheaves

Before answering, please see our policy on resource recommendation questions. Please try to give substantial answers that detail the style, content, and prerequisites of the book or paper (or other resource). Explain what the resource is like…
just-learning
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Is there a physical motivation to study finite fields?

Clearly finite groups are of immense value in physics and these are also substructures of fields. However I never came across any computations involving finite fields at university and so I never learned about them explicitly. Are there some…
Nikolaj-K
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Relation between second cohomology and central extensions

In Blumenhagen's text on conformal field theory, after deriving the central extension of the Witt algebra, namely the Virasoro algebra, $$[L_m,L_n] = (m-n)L_{m+n} + \frac{c}{12}(m^3-m)\delta_{m+n,0}$$ he comments that, above we have computed the…
JamalS
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Flavor symmetry fixes the Higgs branch in any 4D ${\cal N}=2$ QFT

Let us consider two different quantum field theories in 4 dimensional Minkowski spacetime, call them theory A and theory B, with 8 supercharges. (i.e. 4D $\mathcal{N}=2$ theories). Let $G_A$ be the flavor symmetry group of A, and $G_B$ the flavor…
Federico Carta
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What is the importance of studying degeneration on $M_g$

Let $M_g$ be the moduli space of smooth curves of genus $g$. Let $\overline{M_g}$ be its compactification; the moduli space of stable curves of genus $g$. It seems to be important in physics to study the degeneration of certain functions on…
JaP
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Why do you need to count curves on Calabi-Yau manifolds in string theory?

One of the mathematical fields that string theory is said to have had a large bearing on is enumerative geometry which, roughly, deals with counting rational curves on hypersurfaces and its generalisations. From what I could surmise, its main…
Nihar Karve
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Algebraic Geometric Approach to Physical Systems

Is it common to use algebraic geometry for statistical mechanics? More specifically, can we consider the phase space hypersurface consistent with a level of energy as a variety in the affine space and study its properties including volume used to…
VVM
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