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2 results

  • Super-rigid affine Fano varieties

  • Part of
  • Ivan Cheltsov, Adrien Dubouloz, Jihun Park
  • Journal:
    Compositio Mathematica / Volume 154 / Issue 11 / November 2018
    Published online by Cambridge University Press:
    17 October 2018, pp. 2462-2484
    Print publication:
    November 2018
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  • We study a wide class of affine varieties, which we call affine Fano varieties. By analogy with birationally super-rigid Fano varieties, we define super-rigidity for affine Fano varieties, and provide many examples and non-examples of super-rigid affine Fano varieties.

  • Cylinders in singular del Pezzo surfaces

  • Part of
  • Ivan Cheltsov, Jihun Park, Joonyeong Won
  • Journal:
    Compositio Mathematica / Volume 152 / Issue 6 / June 2016
    Published online by Cambridge University Press:
    21 April 2016, pp. 1198-1224
    Print publication:
    June 2016
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  • For each del Pezzo surface $S$ with du Val singularities, we determine whether it admits a $(-K_{S})$-polar cylinder or not. If it allows one, then we present an effective $\mathbb{Q}$-divisor $D$ that is $\mathbb{Q}$-linearly equivalent to $-K_{S}$ and such that the open set $S\setminus \text{Supp}(D)$ is a cylinder. As a corollary, we classify all the del Pezzo surfaces with du Val singularities that admit non-trivial $\mathbb{G}_{a}$-actions on their affine cones defined by their anticanonical divisors.