Constructing moduli spaces of high dimensional algebraic varieties
Introduced by Kollár and Shepherd-Barron, stable varieties are higher-dimensional generalisations of stable curves in algebraic geometry. Their conjectural moduli space classifies smooth projective varieties up to birational equivalence, while also providing a projective compactification. The latter is essential for applying algebraic geometry to the moduli space itself. The EU-funded MODSTABVAR project will construct the coarse moduli space of stable surfaces with fixed volume over the integers. This involves showing the minimal model program for three-dimensional algebraic variety that is projective over a one-dimensional mixed characteristic base. Project results will be very important to the fields of algebraic geometry and the arithmetic of higher-dimensional varieties.
Fields of science
Funding SchemeERC-STG - Starting Grant
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