scholarly journals Deformations of Varieties of General Type

Author(s):  
János Kollár
Keyword(s):  
2021 ◽  
pp. 1-16
Author(s):  
Alexander Dabrowski

A variational characterization for the shift of eigenvalues caused by a general type of perturbation is derived for second order self-adjoint elliptic differential operators. This result allows the direct extension of asymptotic formulae from simple eigenvalues to repeated ones. Some examples of particular interest are presented theoretically and numerically for the Laplacian operator for the following domain perturbations: excision of a small hole, local change of conductivity, small boundary deformation.


Author(s):  
Junyan Cao ◽  
Henri Guenancia ◽  
Mihai Păun

Abstract Given a Kähler fiber space p : X → Y {p:X\to Y} whose generic fiber is of general type, we prove that the fiberwise singular Kähler–Einstein metric induces a semipositively curved metric on the relative canonical bundle K X / Y {K_{X/Y}} of p. We also propose a conjectural generalization of this result for relative twisted Kähler–Einstein metrics. Then we show that our conjecture holds true if the Lelong numbers of the twisting current are zero. Finally, we explain the relevance of our conjecture for the study of fiberwise Song–Tian metrics (which represent the analogue of KE metrics for fiber spaces whose generic fiber has positive but not necessarily maximal Kodaira dimension).


1967 ◽  
Vol 3 (9) ◽  
pp. 631-634 ◽  
Author(s):  
I. �. Gel'ms ◽  
V. I. Yuzefovich ◽  
R. N. Yudinson
Keyword(s):  

1990 ◽  
Vol 196 ◽  
Author(s):  
Chin Liu ◽  
Wong Wei ◽  
Liu Wan Fu

ABSTRACTAt 700°C, with strain rates (έ) of 0.02, 0.05 and 0.08 min−1, the superplastic m-δ curves of T10 steel determined were all of the type (the general type). Their Values of rr (0.241 → 0.252 → 0.267), mL (0288 → 0.241 → 0.252 ),mF (0236 → 0.251 → 0.268), δL(38→. 535 →.58%), and δF (84.7 → 92 → 99%) all increased with increases in value. At the same temperature with έ =0.1 min−1, an ascending type of curve, mL=mwn = mo(=0.245)<mx (=.0.249), δo (=0)= δL > δx (=94%) was obtained from the transformation of δL and mL into the δF and mL of the general type of curve. Similar results have been obtained at 730°C.At 600°,650°, 700° and 730°C, with έ =0.05 min−1 the same general type of curves were obtained. Their values of mo. (0.213 → 0.230 → 0.252 → 0296), mL (0.19 5 → 0.208 → 0.241 → 0.256 ).mF (0.204 → 0.234 → 0.251 → 0.280). δL (44 → 49 → 53.5 → 63.5%)and δF (77 → 81 → 117 percnt) increased with increases in temperature. For the same strain rate, while at 780°C, an ascending type of curve, mL.= mmis = mo (= 0.198) < mF (0.236).δo (=o) = δL < δx (=73%)was obtained from the transformation of the general type of curve in the same way as mentioned above.The shape constants, C values, which vary with strain have been calculated.Symbols: Refer to the List of Symbols.


Author(s):  
Fariba Salehi ◽  
Mohammad Reza Keyvanpour ◽  
Arash Sharifi

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