Details
| Original language | English |
|---|---|
| Pages (from-to) | 678-715 |
| Number of pages | 38 |
| Journal | Algebraic Geometry |
| Volume | 6 |
| Issue number | 6 |
| Publication status | Published - 2019 |
| Externally published | Yes |
Abstract
For a smooth quasi-projective surface X, we construct a series of P-functors between derived categories of Hilbert schemes of points on X using the derived McKay correspondence. They can be considered as analogues of the Nakajima operators. We also study the induced autoequivalences and, in particular, obtain a universal braid relation in the groups of derived autoequivalences of Hilbert squares of K3 surfaces. If we replace the surface X with a smooth curve, our functors become fully faithful and induce a semi-orthogonal decomposition of the derived category of the symmetric quotient stack of the curve.
Keywords
- Autoequivalences of derived categories, Hilbert schemes of points on surfaces, Nakajima operators, Symmetric quotients
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
- Mathematics(all)
- Geometry and Topology
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In: Algebraic Geometry, Vol. 6, No. 6, 2019, p. 678-715.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - P-functor versions of the Nakajima operators
AU - Krug, Andreas
N1 - Funding Information: This work was supported by the SFB/TR 45 of the DFG (German Research Foundation) and, in its final stages, by the research grant KR 4541/1-1 of the DFG.
PY - 2019
Y1 - 2019
N2 - For a smooth quasi-projective surface X, we construct a series of P-functors between derived categories of Hilbert schemes of points on X using the derived McKay correspondence. They can be considered as analogues of the Nakajima operators. We also study the induced autoequivalences and, in particular, obtain a universal braid relation in the groups of derived autoequivalences of Hilbert squares of K3 surfaces. If we replace the surface X with a smooth curve, our functors become fully faithful and induce a semi-orthogonal decomposition of the derived category of the symmetric quotient stack of the curve.
AB - For a smooth quasi-projective surface X, we construct a series of P-functors between derived categories of Hilbert schemes of points on X using the derived McKay correspondence. They can be considered as analogues of the Nakajima operators. We also study the induced autoequivalences and, in particular, obtain a universal braid relation in the groups of derived autoequivalences of Hilbert squares of K3 surfaces. If we replace the surface X with a smooth curve, our functors become fully faithful and induce a semi-orthogonal decomposition of the derived category of the symmetric quotient stack of the curve.
KW - Autoequivalences of derived categories
KW - Hilbert schemes of points on surfaces
KW - Nakajima operators
KW - Symmetric quotients
UR - http://www.scopus.com/inward/record.url?scp=85076398193&partnerID=8YFLogxK
U2 - 10.14231/AG-2019-029
DO - 10.14231/AG-2019-029
M3 - Article
AN - SCOPUS:85076398193
VL - 6
SP - 678
EP - 715
JO - Algebraic Geometry
JF - Algebraic Geometry
SN - 2313-1691
IS - 6
ER -