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3-dimensional sundials

100%

Carlini E., Catalisano M., Geramita A.

Open Mathematics

2011

tom 9

nr 5

949-971

R. Hartshorne and A. Hirschowitz proved that a generic collection of lines on ℙn, n≥3, has bipolynomial Hilbert function. We extend this result to a specialization of the collection of generic lines, by considering a union of lines and 3-dimensional sundials (i.e., a union of schemes obtained by degenerating pairs of skew lines).

On the diffeomorphic type of the complement to a line arrangement in a projective plane

76%

Bogomolov F., Kulikov V.

Open Mathematics

2012

tom 10

nr 2

521-529

We show that the diffeomorphic type of the complement to a line arrangement in a complex projective plane P 2 depends only on the graph of line intersections if no line in the arrangement contains more than two points in which at least two lines intersect. This result also holds for some special arrangements which do not satisfy this property. However it is not true in general, see [Rybnikov G., On the fundamental group of the complement of a complex hyperplane arrangement, Funct. Anal. Appl., 2011, 45(2), 137–148].

Ograniczanie wyników

2 Open Mathematics

1 Bogomolov F.

1 Carlini E.

1 Catalisano M.

1 Geramita A.

1 Kulikov V.

1 2012

1 2011

Wyniki wyszukiwania

3-dimensional sundials

On the diffeomorphic type of the complement to a line arrangement in a projective plane