Explicit Gromov–Hausdorff compactifications of moduli spaces of Kähler–Einstein Fano manifolds

TY - JOUR

T1 - Explicit Gromov–Hausdorff compactifications of moduli spaces of Kähler–Einstein Fano manifolds

AU - Spotti, Cristiano

AU - Sun, Song

PY - 2017

Y1 - 2017

N2 - We exhibit the first non-trivial concrete examples of Gromov-Hausdorff compactifications of moduli spaces of Kähler-Einstein Fano manifolds in all complex dimensions bigger than two (Fano K-moduli spaces). We also discuss potential applications to explicit study of moduli spaces of K-stable Fano manifolds with large anti-canonical volume. Our arguments are based on recent progress about the geometry of metric tangent cones and on related ideas about the algebro-geometric study of singularities of K-stable Fano varieties.

AB - We exhibit the first non-trivial concrete examples of Gromov-Hausdorff compactifications of moduli spaces of Kähler-Einstein Fano manifolds in all complex dimensions bigger than two (Fano K-moduli spaces). We also discuss potential applications to explicit study of moduli spaces of K-stable Fano manifolds with large anti-canonical volume. Our arguments are based on recent progress about the geometry of metric tangent cones and on related ideas about the algebro-geometric study of singularities of K-stable Fano varieties.

U2 - 10.4310/PAMQ.2017.v13.n3.a5

DO - 10.4310/PAMQ.2017.v13.n3.a5

M3 - Journal article

SN - 1558-8599

VL - 13

SP - 477

EP - 515

JO - Pure and Applied Mathematics Quarterly

JF - Pure and Applied Mathematics Quarterly

IS - 3

ER -