The complex singularity exponent is a local invariant of a holomorphic function determined
by the integrability of fractional powers of the function. The log canonical thresholds of …

Algebraic varieties are shapes defined by polynomial equations. Smooth Fano threefolds
are a fundamental subclass that can be thought of as higher-dimensional generalizations of …

There are 105 irreducible families of smooth Fano threefolds, which have been classified by
Iskovskikh, Mori and Mukai. For each family, we determine whether the general member …

Generalised pairs in birational geometry Page 1 EMS Surv. Math. Sci. 8 (2021), 5–24 DOI
10.4171/EMSS/42 © 2021 European Mathematical Society Published by EMS Press This work …

The multiplicity of a nonzero polynomial φ∈ C [z1,···, zn] at the origin O∈ Cn is the
nonnegative integer m such that φ∈ mm\mm+ 1, where m is the maximal ideal of …

arXiv:2012.06495v1 [math.AG] 11 Dec 2020 Existence and boundedness of n-complements
Page 1 arXiv:2012.06495v1 [math.AG] 11 Dec 2020 Existence and boundedness of n-complements …

In this note, we prove a sharp lower bound for the log canonical threshold of a
plurisubharmonic function φ with an isolated singularity at 0 in an open subset of C n. This …

VV d1Á... Ádk F1 ÁÁÁ Fk r PM k, where Fi r PM k is a hypersurface of degree di f 2 and the
integers d1,..., dk satisfy the relation d1 ÁÁÁ dk M k (so that V is of index 1) are birationally …

We address the following question: For which smooth projective varieties the corresponding
affine cone admits an action of a connected algebraic group different from the standard Gm …

This is a survey of recent examples of varieties that are not stably rational. We review the
specialization method based on properties of the Chow group of zero-cycles used in these …