DOI: 10.1017/s1474748026101820 ISSN: 1474-7480
ON THE MAP INDUCED ON HOCHSCHILD HOMOLOGY OF MATRIX FACTORIZATION CATEGORIES BY THE INCLUSION OF A DIVISOR
Ville Nordström Abstract
Given a smooth variety
X
over
C
$\mathbb {C}$
double struck upper C
, a smooth divisor
i
:
Y
↪
X
$i:Y\hookrightarrow X$
i colon upper Y right arrow with hook upper X
and a global function
f
on
X
which vanishes on
Y
and on its critical locus, we compute the map induced on Hochschild homology by the pushforward functor
i
∗
:
D
b
(
Y
)
→
D
a
b
s
(
M
F
(
X
,
f
)
)
$i_{\ast }:D^b(Y)\to D^{abs}(MF(X,f))$
i Subscript asterisk Baseline colon upper D Superscript b Baseline left parenthesis upper Y right parenthesis right arrow upper D Superscript a b s Baseline left parenthesis upper M upper F left parenthesis upper X comma f right parenthesis right parenthesis
in terms of the Hochschild-Kostant-Rosenberg isomorphisms.