6 citations · 15 across the 20 of their papers we have counts for
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Three-dimensional noncommutative Fano minifolds
Konstantin Loginov, Dmitri Orlov
We give a construction of the previously announced family of three-dimensional noncommutative Fano minifolds of Euler degree . We prove that their defining -algebra…
Non-commutative Fano varieties and three-dimensional minifolds
Konstantin Loginov, Dmitri Orlov
We introduce notions of non-commutative Fano varieties and non-commutative minifolds, and study the latter in dimension three. We prove that the Euler matrices of full exceptional…
Unirational del Pezzo surfaces of degree one
Ivan Cheltsov, Konstantin Loginov, Dmitri Orlov +1
We construct explicit unirational del Pezzo surfaces of degree with arithmetic Picard rank one over , , and . Moreover, we prove that e…
Actions of on rationally connected threefolds
Konstantin Loginov
Let . We prove that if is a rationally connected threefold with a faithful action of , then is -birational to the Fermat quartic threefold. If …
Dual complexes of qdlt Fano type models and strong complete regularity
Jihao Liu, Konstantin Loginov
We introduce birational strong complete regularity and strong complete regularity, two numerical invariants for pairs of (relative) Fano type. They are defined using variants of qd…
On the coregularity of del Pezzo surfaces with du Val singularities
Konstantin Loginov, Andrey Trepalin
We compute the coregularity of del Pezzo surfaces with du Val singularities. To this aim, we study the relation between del Pezzo surfaces of degree and elliptic fibrations. It…