Timeline for compute the Kähler moduli of an elliptic curve
Current License: CC BY-SA 2.5
8 events
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| Sep 26, 2021 at 0:44 | comment | added | David Roberts♦ | The updated link to Categorical Mirror Symmetry: The Elliptic Curve in Eric's comment is arxiv.org/abs/math/9801119 | |
| Sep 16, 2010 at 20:38 | comment | added | Eric Zaslow | That question ("some phenomenon") is a bit vague. For more you can read Kontsevich's 1994 ICM paper or this paper by Polishchuk et al: front.math.ucdavis.edu/9801.5119 | |
| Sep 16, 2010 at 1:35 | comment | added | Dan | Thank you for your comments. Let me put the question in another way, how can one verify some phenomenon is mirror symmetry of dimension one? I am reading "motives from diffraction" by Jan Stienstra arxiv.org/abs/math/0511485 | |
| Sep 15, 2010 at 0:32 | comment | added | Eric Zaslow | You're thinking of mirror symmetry now, not pure geometry. In mirror symmetry, the Kahler form is "complexified," referring to a sum of a general (1,1)-form (with no positivity conditions) plus "i" times a geometric Kahler form (which lives in the [real] Kahler cone). More generally, when you integrate the exponential of this form over the surface (i.e. take the pairing with a class in H_2) you get a complex number of modulus less than one, which is the weighting factor for the Gromov-Witten invariant in that homology class. Ideally, the sum over all such numbers will converge. | |
| Sep 14, 2010 at 21:55 | comment | added | Dan | I see what you mean, but I am still confused with the Fubini-Study like Kahler form here. We can choose a volume form (Kahler form) up to scaling, so the volume (Kahler moduli) will be a multiple of some area A. On the other side, the complex structure is normalised as $\tau$ ( say our lattice is $Z+Z\tau$). By the mirror map, $\tau \arrow \rho= b + iA$, my question is how can I fix $b$ and $A$? | |
| Sep 14, 2010 at 21:36 | vote | accept | Dan | ||
| Sep 14, 2010 at 18:43 | history | edited | Eric Zaslow | CC BY-SA 2.5 |
added 5 characters in body
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| Sep 14, 2010 at 18:34 | history | answered | Eric Zaslow | CC BY-SA 2.5 |