The degree of Q-Fano threefolds
We prove that the degree of Fano threefolds with terminal Q-factorial singularities and Picard number one is at most 125/2 and the bound is sharp.
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arXiv subjects
Yu. G. Prokhorov
Publications and source records attributed to Yu. G. Prokhorov.
Toward the second main theorem on complements: from local to global
We prove the boundedness of complements modulo two conjectures: Borisov-Alexeev conjecture and effective adjunction for fibre spaces. We discuss the last conjecture and prove it in two particular cases.
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The first main theorem on complements: from global to local
The aim of this paper is to clarify and generalize techniques of works alg-geom/9711024 (see also math.AG/9810097 and math.AG/9901004). Roughly speaking, we prove that for local Fano contractions the existence of complements can be reduced to the existence of complements for lower dimensional projective Fano varieties.
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Exceptional quotient singularities
A singularity is said to be exceptional (in the sense of V. Shokurov), if for any log canonical boundary, there is at most one exceptional divisor of discrepancy -1. In our previous paper (math.AG/9805004) we found two examples of exceptional canonical singularities: these are quotients by Klein's simple group of order 168 or by its central extension of order 504. Now we classify all the three-dimensional exceptional quotient singularities.
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Klein's group defines an exceptional singularity of dimension 3
We construct two examples of canonical exceptional singularities.
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