Publication

MMP for Enriques pairs and singular Enriques varieties

2026

Abstract

We introduce and study the class of primitive Enriques varieties, whose smooth members are Enriques manifolds. We provide several examples and we demonstrate that this class is preserved under the operations of the Minimal Model Program (MMP). In particular, given an Enriques manifold Y and an effective ℝ -divisor B Y on Y such that the pair ( Y , B Y ) is log canonical, we prove that any ( K Y + B Y ) -MMP terminates with a minimal model ( Y ′ , B Y ′ ) of ( Y , B Y ) , where Y ′ is a ℚ -factorial primitive Enriques variety with canonical singularities. Finally, we investigate the asymptotic theory of Enriques manifolds.

Official source

https://infoscience.epfl.ch/entities/publication/1ca20696-ae1b-4bde-8de7-802309c7a9c6

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2026

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/1ca20696-ae1b-4bde-8de7-802309c7a9c6

About this result

Related concepts (23)

K3 surface

In mathematics, a complex analytic K3 surface is a compact connected complex manifold of dimension 2 with а trivial canonical bundle and irregularity zero. An (algebraic) K3 surface over any field means a smooth proper geometrically connected algebraic surface that satisfies the same conditions. In the Enriques–Kodaira classification of surfaces, K3 surfaces form one of the four classes of minimal surfaces of Kodaira dimension zero. A simple example is the Fermat quartic surface in complex projective 3-space.

Minimal model program

In algebraic geometry, the minimal model program is part of the birational classification of algebraic varieties. Its goal is to construct a birational model of any complex projective variety which is as simple as possible. The subject has its origins in the classical birational geometry of surfaces studied by the Italian school, and is currently an active research area within algebraic geometry. The basic idea of the theory is to simplify the birational classification of varieties by finding, in each birational equivalence class, a variety which is "as simple as possible".

Canonical bundle

In mathematics, the canonical bundle of a non-singular algebraic variety of dimension over a field is the line bundle , which is the nth exterior power of the cotangent bundle on . Over the complex numbers, it is the determinant bundle of the holomorphic cotangent bundle . Equivalently, it is the line bundle of holomorphic n-forms on . This is the dualising object for Serre duality on . It may equally well be considered as an invertible sheaf.