scholarly journals Effective Birational Rigidity of Fano Double Hypersurfaces

2018 ◽  
Vol 4 (3-4) ◽  
pp. 505-521
Author(s):  
Thomas Eckl ◽  
Aleksandr Pukhlikov
Keyword(s):  
Birational Rigidity

scholarly journals Canonical and log canonical thresholds of multiple projective spaces

2019 ◽  
Author(s):  
Aleksandr V. Pukhlikov
Keyword(s):  
Projective Space ◽  
Projective Spaces ◽  
Regularity Conditions ◽  
Large Classes ◽  
Log Canonical Threshold ◽  
Birational Rigidity ◽  
Log Canonical ◽  
Finite Set ◽  
Dimensional Projective Space ◽  
Almost All

AbstractWe show that the global (log) canonical threshold of d-sheeted covers of the M-dimensional projective space of index 1, where $$d\geqslant 4$$d⩾4, is equal to 1 for almost all families (except for a finite set). The varieties are assumed to have at most quadratic singularities, the rank of which is bounded from below, and to satisfy the regularity conditions. This implies birational rigidity of new large classes of Fano–Mori fibre spaces over a base, the dimension of which is bounded from above by a constant that depends (quadratically) on the dimension of the fibre only.

scholarly journals Finite collineation groups and birational rigidity

2019 ◽  
Vol 25 (5) ◽  
Author(s):  
Ivan Cheltsov ◽  
Constantin Shramov
Keyword(s):  
Birational Rigidity ◽  
Collineation Groups

scholarly journals Mori dream spaces and birational rigidity of Fano 3-folds

2016 ◽  
Vol 292 ◽  
pp. 410-445 ◽  
Author(s):  
Hamid Ahmadinezhad ◽  
Francesco Zucconi
Keyword(s):  
Birational Rigidity ◽  
Mori Dream Spaces

scholarly journals Bounds for log canonical thresholds with applications to birational rigidity

2003 ◽  
Vol 10 (2) ◽  
pp. 219-236 ◽  
Author(s):  
Lawrence Ein ◽  
Tommaso de Fernex ◽  
Mircea Mustata
Keyword(s):  
Birational Rigidity ◽  
Log Canonical

scholarly journals Birationally Rigid Complete Intersections with a Singular Point of High Multiplicity

2018 ◽  
Vol 62 (1) ◽  
pp. 221-239 ◽  
Author(s):  
A. V. Pukhlikov
Keyword(s):  
Singular Point ◽  
Complete Intersection ◽  
High Multiplicity ◽  
Complete Intersections ◽  
Birational Rigidity

AbstractWe prove the birational rigidity of Fano complete intersections of index 1 with a singular point of high multiplicity, which can be close to the degree of the variety. In particular, the groups of birational and biregular automorphisms of these varieties are equal, and they are non-rational. The proof is based on the techniques of the method of maximal singularities, the generalized 4n2-inequality for complete intersection singularities and the technique of hypertangent divisors.

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