In order to serve static files in Asp.Net Core you will need following line in Startup.cs method configure:
app.UseStaticFiles();
When deploying in order to show default document, add following line:
app.UseDefaultFiles();
My whole Startup.cs looks like this:
using Microsoft.AspNetCore.Builder;
using Microsoft.AspNetCore.Hosting;
using Microsoft.AspNetCore.Mvc;
using Microsoft.Extensions.Configuration;
using Microsoft.Extensions.DependencyInjection;

namespace AllPics2gMaps
{
  public class Startup
  {
    public Startup(IConfiguration configuration)
    {
      Configuration = configuration;
    }

    public IConfiguration Configuration { get; }

    // This method gets called by the runtime. Use this method to add services to the container.
    public void ConfigureServices(IServiceCollection services)
    {
      services.AddMvc().SetCompatibilityVersion(CompatibilityVersion.Version_2_1);
    }

    // This method gets called by the runtime. Use this method to configure the HTTP request pipeline.
    public void Configure(IApplicationBuilder app, IHostingEnvironment env)
    {
      if (env.IsDevelopment())
      {
        app.UseDeveloperExceptionPage();
      }
      else
      {
        app.UseHsts();
      }

      app.UseHttpsRedirection();
      app.UseMvc();
      app.UseDefaultFiles();
      app.UseStaticFiles();
    }
  }
}
UPDATE; Please note thatStartup.cs has been changed, refer to this article.