Higher-Dimensional Algebraic Geometry studies the classification theory of algebraic
varieties. This very active area of research is still developing, but an amazing quantity of …

It is known that the moduli space of smooth Fano–Mukai fourfolds V_ 18 V 18 of genus 10
has dimension one. We show that any such fourfold is a completion of C^ 4 C 4 in two …

We investigate deformations and characterizations of elliptic Calabi–Yau varieties, building
on earlier works of Wilson and Oguiso. We show that if the second cohomology of the …

Cylinders in Fano varieties Page 1 EMS Surv. Math. Sci. 8 (2021), 39–105 DOI 10.4171/EMSS/44
© 2021 European Mathematical Society Published by EMS Press This work is licensed under …

We construct four different families of smooth Fano fourfolds with Picard rank 1, which
contain cylinders, ie, Zariski open subsets of the form Z * A^ 1 Z× A 1, where Z is a …

We show that the affine cones over a general Fano-Mukai fourfold of genus $ g= 7$, $8 $
and $9 $ are flexible. Equivalently, there is an infinitely transitive action of the special …

arXiv:2304.02293v1 [math.AG] 5 Apr 2023 Page 1 arXiv:2304.02293v1 [math.AG] 5 Apr 2023
THE AFFINE CONES OVER FANO-MUKAI FOURFOLD OF GENUS 7 ARE FLEXIBLE …

The first book on the explicit birational geometry of complex algebraic threefolds arising from
the minimal model program, this text is sure to become an essential reference in the field of …

Let X be a smooth, complex Fano 4-fold, and ρ X its Picard number. We show that if ρ X> 12,
then X is a product of del Pezzo surfaces. The proof relies on a careful study of divisorial …

Let X be a smooth complex Fano variety. We study 'quasi-elementary'contractions of fiber
type of X, which are a natural generalization of elementary contractions of fiber type. If f: X→ …