We calculate the integers d such that a general surface X_d in P^3 of degree d contains an arithmetically Gorenstein set of points with a linear syzygy matrix of size 2a+1. This condition is equivalent to X_d being defined by the pfaffian of a skew-symmetric matrix whose entries are linear except possibly a row and a column. We prove that this takes place for all d>a if a<11. Conversely, for a>10, we show that the condition holds if and only if d is contained in the interval [a+1,15].
Chiantini, L., Faenzi, D. (2009). On general surfaces defined by an almost linear pfaffian. GEOMETRIAE DEDICATA, 142, 91-107 [10.1007/s10711-009-9360-7].
On general surfaces defined by an almost linear pfaffian
CHIANTINI, LUCA;
2009-01-01
Abstract
We calculate the integers d such that a general surface X_d in P^3 of degree d contains an arithmetically Gorenstein set of points with a linear syzygy matrix of size 2a+1. This condition is equivalent to X_d being defined by the pfaffian of a skew-symmetric matrix whose entries are linear except possibly a row and a column. We prove that this takes place for all d>a if a<11. Conversely, for a>10, we show that the condition holds if and only if d is contained in the interval [a+1,15].
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https://hdl.handle.net/11365/23415
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