# Questions tagged [mirror-symmetry]

Use for questions about mirror symmetry in theoretical/mathematical physics. Associate with [tag:mathematical-physics] if necessary.

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### Must all lines of symmetry for a shape pass through the same point?

Must all lines of symmetry for a shape pass through the same point? I'm unable to think of a shape that doesn't follow this rule but can't come up with rigorous proof for this. By shape I mean any ...
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1 vote
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### Bondal-Orlov conjecture on Calabi-Yau varieties

Recently, I am trying to study the various progress made on the Bondal-Orlov conjecture: Birational Calabi-Yau varieties $\implies$ Equivalent derived categories. I have started reading the paper by ...
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### How to construct the Green's function solution for the barotropic Rossby wave eq with Dirichlet b.c.?

The linear differential equation I have been working on is the barotropic Rossby wave equation:  L\psi=(\frac{\partial}{\partial t}\nabla^2+\beta\frac{\partial}{\partial x} )\psi=\delta(\vec{x}-\vec{...
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### S-curve Graph Mirror

I have an s-curve equation that uses cosine. Any trigonometric function is allowed but I can't use exponential or logarithmic equations as they don't perform to what is required. The cosine equation ...
1 vote
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### A variety is the moduli space of structure sheaves of points

In the last paragraph of the first page of this paper, it is mentioned that an $n$-dimensional Calabi-Yau manifold $X$ is the moduli space of structure sheaves of its points and I am not really sure ...
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### Introductory papers in Mirror Symmetry for algebraic geometry students

Assuming that a student knows algebraic geometry at the level of Cox's (1) Ideals, Varieties and Algorithms and (2) Toric Varieties What are some good papers (meaning, suitable in light of (1) and (2))...
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### Moduli space of special Lagrangians

I'm currently reading Auroux's Mirror Symmetry and T-duality in the Complement of the Anticanonical Divisor and Special Lagrangian Fibrations, Wall-crossing, and Mirror Symmetry back and forth. I'm ...
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### Convert from one segment to another in 2D-coordinate system

Given a 2D-coordinate system where we only look at the area between 0-1 on both, x and y axis. How can I divide that system into n segments and mirror a point at p(0.5,0.5), so that all points are ...
1 vote
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### 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
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### 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 ...
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### 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 ...
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### 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....
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### 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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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ... 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 ...
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### 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 ... 