TY - JOUR

T1 - Existence of simply connected algebraic surfaces of general type with positive and zero indices

AU - Moishezon, Boris

AU - Teicher, M.

PY - 1986

Y1 - 1986

N2 - In the classification problem of algebraic surfaces of general type, an important conjecture states that for simply connected such surfaces Chern numbers satisfy the inequality c12 ≤ 2c2 (or equivalently, the index τ ≤ 0). We disprove this conjecture by computing fundamental groups of Galois coverings corresponding to generic CP2 projections of projective embeddings of CP1 × CP1 related to linear systems [unk]al1 + bl2[unk], a ≥ 3, b ≥ 2. Also, we proved the existence of simply connected minimal surfaces of general type with zero index (e.g., c12 = 2c2). Previously, it was conjectured that these are exactly the surfaces uniformizable in the polydisk. So this conjecture is also disproved.

AB - In the classification problem of algebraic surfaces of general type, an important conjecture states that for simply connected such surfaces Chern numbers satisfy the inequality c12 ≤ 2c2 (or equivalently, the index τ ≤ 0). We disprove this conjecture by computing fundamental groups of Galois coverings corresponding to generic CP2 projections of projective embeddings of CP1 × CP1 related to linear systems [unk]al1 + bl2[unk], a ≥ 3, b ≥ 2. Also, we proved the existence of simply connected minimal surfaces of general type with zero index (e.g., c12 = 2c2). Previously, it was conjectured that these are exactly the surfaces uniformizable in the polydisk. So this conjecture is also disproved.

UR - http://www.pnas.org/content/83/18/6665.short

M3 - Article

SN - 0027-8424

VL - 83

SP - 6665

EP - 6666

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

IS - 18

ER -