Critical dimensions of the string theories and the dualizing sheaf on the moduli space of (super) curves

1986 ◽  
Vol 20 (3) ◽  
pp. 244-246 ◽  
Author(s):  
Yu. I. Manin
Keyword(s):  
Moduli Space ◽  
Critical Dimensions ◽  
Dualizing Sheaf ◽  
String Theories

scholarly journals Normal functions and the height of Gross-Schoen cycles

2014 ◽  
Vol 214 ◽  
pp. 53-77 ◽  
Author(s):  
Robin De Jong
Keyword(s):  
Line Bundle ◽  
Moduli Space ◽  
The Self ◽  
Compact Type ◽  
Stable Curves ◽  
Normal Functions ◽  
Chern Form ◽  
Bloch Line ◽  
Pointed Curve ◽  
Dualizing Sheaf

AbstractWe prove a variant of a formula due to Zhang relating the Beilinson– Bloch height of the Gross–Schoen cycle on a pointed curve with the self-intersection of its relative dualizing sheaf. In our approach, the height of the Gross–Schoen cycle occurs as the degree of a suitable Bloch line bundle. We show that the Chern form of this line bundle is nonnegative, and we calculate its class in the Picard group of the moduli space of pointed stable curves of compact type. The basic tools are normal functions and biextensions associated to the cohomology of the universal Jacobian.

New critical dimensions for string theories

1987 ◽  
Vol 284 ◽  
pp. 397-422 ◽  
Author(s):  
A. Bilal ◽  
J.-L. Gervais
Keyword(s):  
Critical Dimensions ◽  
String Theories

The appearance of critical dimensions in regulated string theories (II)

1986 ◽  
Vol 275 (2) ◽  
pp. 161-184 ◽  
Author(s):  
J. Ambjørn ◽  
B. Durhuus ◽  
J. Fröhlich
Keyword(s):  
Critical Dimensions ◽  
String Theories

scholarly journals Normal functions and the height of Gross-Schoen cycles

2014 ◽  
Vol 214 ◽  
pp. 53-77
Author(s):  
Robin De Jong
Keyword(s):  
Line Bundle ◽  
Moduli Space ◽  
The Self ◽  
Compact Type ◽  
Stable Curves ◽  
Normal Functions ◽  
Chern Form ◽  
Bloch Line ◽  
Pointed Curve ◽  
Dualizing Sheaf

AbstractWe prove a variant of a formula due to Zhang relating the Beilinson– Bloch height of the Gross–Schoen cycle on a pointed curve with the self-intersection of its relative dualizing sheaf. In our approach, the height of the Gross–Schoen cycle occurs as the degree of a suitable Bloch line bundle. We show that the Chern form of this line bundle is nonnegative, and we calculate its class in the Picard group of the moduli space of pointed stable curves of compact type. The basic tools are normal functions and biextensions associated to the cohomology of the universal Jacobian.

UNIFICATION OF YANG-MILLS THEORY AND SUPERSTRINGS

1988 ◽  
Vol 03 (07) ◽  
pp. 1663-1673 ◽  
Author(s):  
GEORGE F. CHAPLINE
Keyword(s):  
Gauge Group ◽  
Complex Manifold ◽  
Gauge Invariance ◽  
Critical Dimension ◽  
Conformal Anomaly ◽  
Critical Dimensions ◽  
Yang Mills ◽  
Mathematical Interpretation ◽  
String Theories

A scheme is suggested for constructing new types of superstrings with critical dimensions D=10 and D=26 by introducing Yang-Mills potentials as auxiliary fields. The Yang-Mills gauge group is fixed by the critical dimension and the requirement that it must be spontaneously broken in order that the conformal anomaly cancel. For critical dimension D=26 a superstring may exist with an unbroken SU(3)×SU(2)×U(1) gauge invariance. This superstring has N=2 supersymmetry and is constrained to move on a nontrivial 24-dimensional complex manifold. Both the first quantized and second quantized versions of these string theories give promise of an interesting mathematical interpretation.

scholarly journals The dualizing sheaf on first-order deformations of toric surface singularities

2019 ◽  
Vol 2019 (753) ◽  
pp. 137-158 ◽  
Author(s):  
Klaus Altmann ◽  
János Kollár
Keyword(s):  
Moduli Space ◽  
General Type ◽  
Surfaces Of General Type ◽  
Toric Surface ◽  
First Order ◽  
Surface Singularities ◽  
Quotient Singularities ◽  
Infinitesimal Deformations ◽  
Cyclic Quotient Singularities ◽  
Dualizing Sheaf

AbstractWe explicitly describe infinitesimal deformations of cyclic quotient singularities that satisfy one of the deformation conditions introduced by Wahl, Kollár–Shepherd-Barron (KSB) and Viehweg. The conclusion is that in many cases these three notions are different from each other. In particular, we see that while the KSB and the Viehweg versions of the moduli space of surfaces of general type have the same underlying reduced subscheme, their infinitesimal structures are different.

The appearance of critical dimensions in regulated string theories

1986 ◽  
Vol 270 ◽  
pp. 457-482 ◽  
Author(s):  
J. Ambjørn ◽  
B. Durhuus ◽  
J. Fröhlich ◽  
P. Orland
Keyword(s):  
Critical Dimensions ◽  
String Theories
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