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 -