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Igusas

Igusas is a surname of Japanese origin, and in mathematics the term is associated with several concepts named after the Japanese-born mathematician Jun-ichi Igusa (1924–2013). Igusa’s work spanned topology, number theory, and algebraic geometry, and his name appears in a number of foundational constructions in these fields.

One prominent use is the Igusa zeta function. Introduced by Igusa, it studies p-adic integrals associated with

Another key area is the Igusa invariants for genus 2 curves. These invariants I2, I4, I6, and

Igusa varieties and the associated Igusa towers appear in the study of moduli problems for abelian varieties

Beyond these, Igusa’s influence extends to other constructions and invariants in number theory and algebraic geometry.

a
polynomial
and
encodes
information
about
singularities
of
the
polynomial.
The
resulting
zeta
function
is
a
rational
function
in
the
p-adic
variable
p^{-s},
and
its
poles
and
coefficients
reflect
arithmetic
and
geometric
properties
of
the
polynomial.
I10
arise
from
Siegel
modular
forms
and
provide
a
complete
set
of
moduli
for
genus
2
curves
up
to
isomorphism
over
an
algebraically
closed
field.
They
are
important
in
algorithms
for
classifying
and
recognizing
genus
2
curves
in
computational
algebraic
geometry.
with
extra
p-adic
level
structure.
These
objects
arise
in
the
arithmetic
of
Shimura
varieties
and
in
p-adic
uniformization
theory,
where
they
facilitate
analysis
of
reductions
modulo
p
and
the
interaction
between
automorphic
forms
and
algebraic
geometry
at
p.
The
name
continues
to
appear
in
contemporary
research
as
a
legacy
of
his
contributions
to
the
field.