Questions tagged [mirror-symmetry]
Use for questions about mirror symmetry in theoretical/mathematical physics. Associate with [tag:mathematical-physics] if necessary.
30
questions
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0answers
25 views
Find mirror value of an alternating function.
Let:
$$g(2n) = f(2n) + c$$
$$g(2n-1) = -f(2n-1) + c$$
$$n \in \Bbb{N}$$
Known:
$g(x)$
Unknown:
$f(x)$, $c$
$$c = ?$$
Image:
How to calculate $c$, is there any useful math property ?
I will apriciate ...
0
votes
0answers
28 views
Mirror Symmetry References
For someone comfortable with Hartshorne's book chapters 2 and 3 which references would be good to learn mirror symmetry (specially the homological flavor), GW invariants and related problems? I intend ...
1
vote
0answers
45 views
Unambiguous geometry terms for specific kinds of circular symmetry
I'm writing a paper on asymmetries in the human visual system and want to ensure that I am using correct/unambiguous terminology to describe the asymmetries in question. Unfortunately, I've had ...
0
votes
1answer
32 views
Pre-calc algebraic method for predicting symmetry
I am looking for an algorithm that can be used on any equation that contains polynomials containing x and y to determine if reflective or rotational symmetries exist. If it is possible, I would like a ...
0
votes
0answers
27 views
What is this kind of symmetry called?
What is the formal way to describe an object that has reflection symmetry about two orthogonal axes?
For instance, any rectangle is symmetric about the axis parallel to its long edge, and also the one ...
2
votes
0answers
213 views
How graduate students get to work in homological mirror symmetry
My question is probably an odd one here but I would very much like to work in Homological Mirror Symmetry. An example of a course I'd like to be able to take and understand is https://faculty.math....
0
votes
0answers
40 views
Size of image in plane mirror?
It is said that the size of an image in a plane mirror is the same as the original object . How can this be true if by ray diagrams the mirror height only needs to be 1/2 the height of the object to ...
0
votes
1answer
88 views
Find Reflection of A point with respect to a line mirror in 3D
I need to find the reflection of point $P(1,2,3)$ w.r.t line mirror $(x-1)/2 =(y-1)/3 = (z+1)/1$
I know one method to do it i.e by first finding the foot of perpendicular of P on the line by using ...
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0answers
7 views
Point Group of a basic cell within a TV Frieze group
Unfortunately my lecturer refuses to reply to emails so I need to ask this question here so I can hopefully clear some things up. I also don't know how standard the notation we are learning is so I ...
0
votes
0answers
26 views
Genus of a curve? (Mirror Symmetry book)
I'm reading Chapter 6 of Mirror Symmetry book.
In Example 6.1.1
"A degree 3 polynomial f in $\mathbb P^2$ determines a curve of genus
$g = \binom{3−1}{2} = 1$ that has the structure (induced from ...
2
votes
0answers
43 views
Is $(x,y)\rightarrow (-x,-y)$ an inversion transformation?
Does anyone know whether $(x,y)\rightarrow (-x,-y)$ is an inversion transformation or not?
I know that the standard inversion (parity) transformation in two dimensions should be something like $(x,y)\...
2
votes
1answer
39 views
Defining asymmetries in Turing's reaction-diffusion paper
I'm reading Alan Turing's paper titled The Chemical Basis of Morphogenesis and there is a section in it with mathematical definitions that mystify me. I'm guessing that Turing tried to keep ...
4
votes
0answers
56 views
Why is a DG-enhancement of the derived bounded category of coherent sheaves an enhancement?
In order to make mirror symmetry more compatible with homological machinery, I understand it is common to give the derived bounded category on a variety a "DG-enhancement" by keeping around the data ...
3
votes
0answers
110 views
Fibrating $X=\Bbb R^2 / \{0\}$ by breaking up the space with hyperbola?
Attending graduate school this Fall and need to understand fibrations better. I will be taking geometry and algebra. I've read a neat article Quanta Magazine Article on the topic of mirror worlds and ...
2
votes
0answers
28 views
Why Lagrangians of two (real) torus are lines?
I am reading an article on Mirror Symmetry, where an example is given : the two (real) dimensional torus.
My question is a basic one : taking the symplectic form (if ones focuses on the symplectic ...
1
vote
0answers
326 views
Book References about Complex Geometry
I took an introductory course in differential geometry, and now I take an advanced course about mirror symmetry and Calabi-Yau manifolds. I know this is way out of my league but I just want to have a ...
3
votes
1answer
287 views
Mirror Symmetry of Calabi-Yau Surfaces?
This isn't a terribly refined question, but more broad-brush: are there nice results on explicit mirror pairs of certain Calabi-Yau surfaces? In particular, I'm curious if we know the mirror partners ...
2
votes
1answer
131 views
What is mirror of symplectic $\mathbb{CP}^{2}$?
As far as I understand, mirror symmetry is an involution on the set of Calabi-Yau manifolds which acts at Hodge numbers by $h^{p,q} \leftrightarrow h^{q,p}$.
Kontsevich in 1994 conjectured an ...
3
votes
1answer
213 views
First Chern class of toric manifolds
I have been reading a Mirror Symmetry monograph, and its physical arguments seem to imply that all toric manifolds have semipositive-definite first Chern class.
Is this true, and if yes, how does ...
5
votes
1answer
731 views
Prerequisites for book “mirror symmetry and algebraic geometry” by Cox and Katz
As the title suggest, I am trying to read the book mentioned, but I find that it uses a lot of material that I don't know yet. For example, it uses toric geometry and polytopes, topics that I've never ...
6
votes
1answer
326 views
Mirror Symmetry of Elliptic Curve
I'm a little bit unsure about the mirror symmetry statement for elliptic curves; specifically, how the flipping of the Kähler and complex moduli works. Perhaps I should say at the outset, the reason ...
2
votes
0answers
42 views
Mathematical terminology about Holomorphic vector bundle over Grassmanian.
This question is relevant to Mirror symmetry and moduli space.
The linear sigma model in $U(k)$ with $Nk$ chiral fields vacua equation can be reduced as
\begin{align}
\sum_{i,j=1}^k \left(\sum_s^N \...
2
votes
0answers
21 views
Moduli space about $CP^{N-1}$ and $T^* CP^{N-1}$.
For complex $\phi$ in $U(1)$ gauge theory, we have
\begin{align}
|\phi_1|^2 + |\phi_2|^2 +\cdots |\phi_N|^2 =r
\end{align}
This equation $|\phi|^2=r$, describes sphere $S^{2N-1}$. Dividing the space ...
8
votes
0answers
268 views
The Kähler form and the anticanonical line bundle
Let $M$ be a Kähler manifold. We say that $M$ is Fano if the anticanonical line bundle $K_M^*$ of $M$ is ample (or positive).
On the other hand, I sometimes see the following definition (or ...
20
votes
3answers
2k views
Areas of contemporary Mathematical Physics
I have often heard that some developments in Physics such as Gauge Theory, String Theory, Twistor Theory, Loop Quantum Gravity etc. have had a significant impact on pure mathematics especially ...
5
votes
1answer
213 views
Construction of virtual class at Homological Mirror Symmetry
In Homological Mirror Symmetry it is necessary to integrate cohomology class at stable moduli.
For this, we can define virtual dimension that stable moduli space should have, and at moduli defined at ...
7
votes
1answer
691 views
Reference for Fukaya Categories and Homological Mirror Symmetry
What references are there for learning Fukaya categories (specifically, good references for self-study)?
In addition, any references with an eye toward homological mirror symmetry would be greatly ...
7
votes
2answers
1k views
Reference request: toric geometry
What is a good book on algebraic geometry, with focus on toric varieties, similar both in the philosophy and in the prestige of the authors to Modern Geometric Structures and Fields
by Novikov and ...
11
votes
1answer
2k views
Mathematics and Physics prerequisites for mirror symmetry
I am a physics undergrad interested in Mathematical Physics. I am more interested in the mathematical side of things, and interested to solve problems in mathematics inspired by physics maybe with the ...
4
votes
1answer
330 views
About Homological Mirror Symmetry
Why in homological mirror symmetry, we restrict us to a projective variety (Calabi-Yau manifold)? Because in physics we don't need this condition.
What's the general picture for general Calabi-Yau ...
