Numerical obstructions to abelian surfaces in toric Fano 4-folds

نویسنده

G. K. Sankaran

چکیده

Theorem 1 Suppose X is a smooth toric Fano 4-fold. Then X admits a totally nondegenerate abelian surface if X = P4, if X = P1 × P3 (type B4), or if X is a product of two smooth toric Del Pezzo surfaces (i.e. of type C4, D13, H8, L7, L8, L9, Q10, Q11, K4, U5, S2 × S2, S2 × S3 or S3 × S3). Otherwise there is no such embedding, unless possibly X is of type C3, D7, D10, D11, D14, D17, D18, G3, G4, G5, L11, L13, I9, Q16, U8, V4, W, Z1 or Z2.

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