Fano Varieties with Small Non-klt Locus
Copyright policy )Fano Varieties with Small Non-klt Locus
Let X be a Fano variety of index k such that the non-klt locus Nklt(X) is not empty. We prove that Nklt(X) has dimension at least k-1 and equality holds if and only if Nklt(X) is a linear projective space P^{k-1}. In this case X has lc singularities and is a generalised cone with Nklt(X) as vertex. If X has lc singularities and Nklt(X) has dimension k we describe the non-klt locus and the global geometry of X. Moreover, we construct examples to show that all the classification results are effective.
20 pages, changed metadata
14J45, 14E30, 14D06, 14J40, 14M22, Fano varieties, Singularities, Mathematics - Algebraic Geometry, [MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG], FOS: Mathematics, Algebraic Geometry (math.AG)
14J45, 14E30, 14D06, 14J40, 14M22, Fano varieties, Singularities, Mathematics - Algebraic Geometry, [MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG], FOS: Mathematics, Algebraic Geometry (math.AG)
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