type of StdSchedulerFactory.GetDefaultScheduler() is task not IScheduler,so I got following error.
how can I fix this?
type of StdSchedulerFactory.GetDefaultScheduler() is task not IScheduler,so I got following error.
how can I fix this?
You have to await for the result. I suppose you are not awaiting. 
StdSchedulerFactory factory = new StdSchedulerFactory(props);
IScheduler scheduler = await factory.GetScheduler();
await scheduler.Start();
Here is complete example from Quartz docs.
private static async Task RunProgram()
    {
        try
        {
            // Grab the Scheduler instance from the Factory
            NameValueCollection props = new NameValueCollection
            {
                { "quartz.serializer.type", "binary" }
            };
            StdSchedulerFactory factory = new StdSchedulerFactory(props);
            IScheduler scheduler = await factory.GetScheduler();
            // and start it off
            await scheduler.Start();
            // some sleep to show what's happening
            await Task.Delay(TimeSpan.FromSeconds(60));
            // and last shut down the scheduler when you are ready to close your program
            await scheduler.Shutdown();
        }
        catch (SchedulerException se)
        {
            await Console.Error.WriteLineAsync(se.ToString());
        }
    }
