## 63 Citations

A geometric characterization of toric varieties

- Mathematics
- 2018

We prove a conjecture of Shokurov which characterises toric varieties using log pairs.

The Sarkisov program for Mori fibred Calabi-Yau pairs

- Mathematics
- 2015

We prove a version of the Sarkisov program for volume preserving birational maps of Mori fibred Calabi-Yau pairs valid in all dimensions. Our theorem generalises the theorem of Usnich and Blanc on…

Birational Geometry of Projective Varieties and Directed Graphs

- Mathematics
- 2014

We give a brief introduction to some of the results in the Minimal Model Programme using the elementary theory of directed graphs.

BIRATIONAL RIGIDITY OF FANO 3-FOLDS AND MORI DREAM SPACES

- Mathematics
- 2014

We highlight a relation between the existence of Sarkisov links and the finite generation of (certain) Cox rings. We introduce explicit methods to use this relation in order to prove birational…

Sarkisov Program for Generalized Pairs

- Mathematics
- 2018

In this paper we show that any two birational $\mathbb Q$-factorial generalized KLT pairs are related by a finite sequence of Sarkisov links.

INVARIANCE OF CERTAIN PLURIGENERA FOR SURFACES IN MIXED CHARACTERISTICS

- MathematicsNagoya Mathematical Journal
- 2020

We prove the deformation invariance of Kodaira dimension and of certain plurigenera and the existence of canonical models for log surfaces which are smooth over an integral Noetherian scheme $S$.

The real plane Cremona group is an amalgamated product

- MathematicsAnnales de l'Institut Fourier
- 2021

We show that the real Cremona group of the plane is a nontrivial amalgam of two groups amalgamated along their intersection and give an alternative proof of its abelianisation.

Finite groups of birational transformations

- Mathematics
- 2021

We survey new results on finite groups of birational transformations of algebraic varieties. Primary 14E07; Secondary 14J50, 14J45, 14E30 Cremona group, birational transformation, Fano variety,…

THE REAL PLANE CREMONA GROUP IS A NON-TRIVIAL AMALGAM

- Mathematics
- 2019

We show that the real Cremona group of the plane is a non-trivial amalgam of two groups amalgamated along their intersection and givean alternative proof of its abelianisation.

## References

SHOWING 1-10 OF 11 REFERENCES

Existence of minimal models for varieties of log general type

- Mathematics
- 2006

Assuming finite generation in dimension n − 1, we prove that pl-flips exist in dimension n.

Flops Connect Minimal Models

- Mathematics
- 2007

A result by Birkar-Cascini-Hacon-McKernan together with the boundedness of length of extremal rays implies that different minimal models can be connected by a sequence of flops. A flop of a pair (X,…

Log Sarkisov Program

- Mathematics
- 1995

The purpose of this paper is two-fold. The first is to give a tutorial introduction to the Sarkisov program, a 3-dimensional generalization of Castelnuovo-Nother Theorem ``untwisting" birational maps…

Mori dream spaces and GIT.

- Mathematics
- 2000

The main goal of this paper is to study varieties with the best possible Mori theoretic properties (measured by the existence of a certain decomposition of the cone of effective divisors). We call…

"J."

- Philosophy
- 1890

however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)…

Factoring birational maps of threefolds after Sarkisov

- Internat . J . Math .
- 1997

Factoring birational maps of threefolds after Sarkisov

- Internat . J . Math .
- 1997

Factoring birational maps of threefolds after Sarkisov

- J. Algebraic Geom
- 1995

A and V given by (4.1). Pick points Θ 0 ∈ A A,φ@BULLETf (V ) and Θ 1 ∈ A A,ψ@BULLETg (V ) belonging to the interior of L A (V )

- A and V given by (4.1). Pick points Θ 0 ∈ A A,φ@BULLETf (V ) and Θ 1 ∈ A A,ψ@BULLETg (V ) belonging to the interior of L A (V )