Existence of minimal models for varieties of log general type

By C. Birkar, Paolo Cascini, Christopher D. Hacon, J. McKernan. 2006

1,652 citations recorded by the source corpus.

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

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1b337fa52aa8c597f729f7a0c6c0a904d2d7a3be

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Building blocks of polarized endomorphisms of normal projective varieties (2016, methodology): “By [2], we can run (KY + tjA)-MMP on Y with scaling of A”
Jordan property for Cremona groups (2012, background): “Actually, [2] treats the case when G is trivial, but adding a finite group action does not make a big difference.”
Kähler–Einstein Metrics on Stable Varieties and log Canonical Pairs (2013, methodology): “We also recall that in the case of varieties of log general type with log terminal singularities (which in our notation means that D lc vanishes) the ﬁnite generation in question was established in the seminal work [ BCHM10 ] and K¨ahler-Einstein metrics were ﬁrst constructed in [ EGZ09 ].”
Building blocks of étale endomorphisms of complex projective manifolds (2009, background): “The recent paper [3] has announced a proof of the existence of minimal models of varieties of general type even in a relative setting.”
Semi-stable minimal model program for varieties with trivial canonical divisor (2010, methodology): “coeﬃcient of E with respect to (X,∆) is denoted by a(E,X,∆). We work over C, the complex number ﬁeld, throughout this paper. We freely use the standard terminology on the log minimal model program in [BCHM] and [KM]. 2. Easytermination lemma In this section, we give a suﬃcient condition for the term”
Which powers of holomorphic functions are integrable (2008, methodology): “The relevant parts of the MMP are now known in all dimensions [BCHM06].”
On images of Mori dream spaces (2011, background): “be a Q-factorial normal projective variety and ∆i (i= 1,2,...,N) be eﬀective divisors on Xsuch that (X,∆i) are klt. We consider the case when the cone C spanned by the divisors (KX + ∆i) is a MDR. In [BCHM], it was proven that it is the case when the boundary divisors ∆i are big. This is expected to”
Abundance theorem for numerically trivial log canonical divisors of semi-log canonical pairs (2010, methodology): “l canonical bundle formula (cf. [A]). Hence we consider the conjecture in the case where (X,∆) is log canonical and KX + ∆ ≡ 0. In Section 3, we prove the following theorem by using their results and [BCHM]: Theorem 1.2 (=Theorem 3.1). Let (X,∆) be a projective log canonical pair. Suppose that KX +∆”
Log minimal model program for the moduli space of stable curves: The first flip (2008, background): “g=22and g≥ 24[Far06, HM82, EH86]. In these cases, we can consider the canonical ring ⊕n≥0Γ(n(KM g )). which is ﬁnitely generated by a fundamental conjecture of birational geometry, recently proven in [BCHM06]. Then the corresponding projective variety Proj⊕n≥0 Γ(n(KM g )) is birational to Mg and is ”
The Minimal Model Program for the Hilbert Scheme of Points on P^2 and Bridgeland Stability (2012, background): “sequence of ﬂips and divisorial contractions that relate M to M(D). (3) Finally, if possible, ﬁnd a modular interpretation of M(D). Inspired by the seminal work of Birkar, Cascini, Hacon and McKernan [BCHM], there has been recent progress in understanding the minimal model program for many important”