I actually had the same problem as you! I have the same processor and compiler and everything.
The problem happens because GCC 9.3.0 (the version of GCC that build-essential on Ubuntu 20.04 comes with) doesn't recognize tigerlake as a valid architecture (perhaps because it is new... I'm not entirely sure why it's this way).
The solution is very simple: Download GCC 10! GCC 10 accepts -march=tigerlake and -mtune=tigerlake as valid flags.
(This is the solution that enabled me to compile Sage 9.3 from source without any trouble whatsoever.)
Here are the commands you have to run: (The dollar signs convey the command prompt)
$sudo apt update
$sudo apt install gcc-10 g++-10
I found out yesterday, while building Sage 9.3, that gfortran is necessary because SciPy uses it, and SciPy seems to be an integral part of Sage. So, if you plan to build SciPy, download gfortran-10 as well:
$sudo gfortran-10
Now you have the compilers, but you still need to make
gcc,
g++, and
gfortran to point to the newest versions of the software. This is where
update-alternatives comes into play. Run these commands (
courtesy of this website):
$sudo update-alternatives --install /usr/bin/gcc gcc /usr/bin/gcc-10 100 --slave /usr/bin/g++ g++ /usr/bin/g++-10 --slave /usr/bin/gcov gcov /usr/bin/gcov-10
$sudo update-alternatives --install /usr/bin/gcc gcc /usr/bin/gcc-9 90 --slave /usr/bin/g++ g++ /usr/bin/g++-9 --slave /usr/bin/gcov gcov /usr/bin/gcov-9
These commands set gcc-10 and g++-10 to a priority of 100 and set gcc-9 and g++-9 to a priority of 90 so that by default, gcc-10 and g++-10 are used whenever gcc/g++ is called. (Of course, this can be changed later on, if desired). As the website suggests, you can run sudo update-alternatives --config gcc to make sure that the action was performed correctly.
The same thing needs to be done for gfortran, if you plan on building SciPy from source:
$sudo update-alternatives --install /usr/bin/gfortran gfortran /usr/bin/gfortran-10 100
$sudo update-alternatives --install /usr/bin/gfortran gfortran /usr/bin/gfortran-9 90
Like before, you can run sudo update-alternatives --config gfortran to make sure that the action was performed correctly.
I hope this helps!