Białynicki-Birula decomposition for reductive groups in positive characteristic

Jelisiejew, Joachim; Sienkiewicz, Łukasz

doi:10.1016/j.matpur.2021.05.010

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“…Białynicki-Birula decompositions. The general theory of Białynicki-Birula decompositions is beautiful but quite complicated, see [JS19,JS21,Tha96]. We would like to apply it to the standard scalar torus action on the Hilbert scheme.…”

Section: Introductionmentioning

confidence: 99%

Elementary components of Hilbert schemes of points

Jelisiejew

2019

J. London Math. Soc.

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Consider the Hilbert scheme of points on a higher dimensional affine space. Its component is elementary if it parameterizes irreducible subschemes. We characterize reduced elementary components in terms of tangent spaces and provide a computationally efficient way of finding such components. As an example, we find an infinite family of elementary and generically smooth components on the affine four-space. We analyse singularities and formulate a conjecture which would imply the non-reducedness of the Hilbert scheme. Our main tool is a generalization of the Bia lynicki-Birula decomposition for this singular scheme.

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Section: Introductionmentioning

confidence: 99%

Elementary components of Hilbert schemes of points

Jelisiejew

2019

J. London Math. Soc.

View full text Add to dashboard Cite

show abstract

Białynicki-Birula decomposition for reductive groups in positive characteristic

Cited by 1 publication

References 12 publications

Elementary components of Hilbert schemes of points

Elementary components of Hilbert schemes of points

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