Unexpected but recurrent phenomena for Quot and Hilbert schemes of points · arXivDesk
2403.03146Mar 5, 2024Added a statement proving that the nested Hilbert scheme of a smooth surface admits generically non-reduced components. Final version, to appear in Rend. Sem. Mat. Univ. Politec. Torino
Unexpected but recurrent phenomena for Quot and Hilbert schemes of points
Franco Giovenzana, Luca Giovenzana, Michele Graffeo, Paolo Lella
We investigate some aspects of the geometry of two classical generalisations of the Hilbert schemes of points. Precisely, we show that parity conjecture for QuotrdA3 already fails for d=8 and r=2
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and that lots of the elementary components of the nested Hilbert schemes of points on smooth quasi-projective varieties of dimension at least 4 are generically non-reduced. We also deduce that nested Hilbert schemes of points on smooth surfaces have generically non-reduced components. Finally, we give an infinite family of elementary components of the classical Hilbert schemes of points.