Scheme And Cohomology

we introduce the basic definitions and properties of scheme and cohomology, then apply the language of scheme and cohomology to describe the curves from genus 0 to genus 6. Firstly, we give the basic definitions of scheme and some properties which we usually use. Secondly, we describe the process of computing the cohomology group of projective space which is enough for most cases. We also introduce divisor and invertible sheaf which are essential for the following stud of curves. Finally, we apply the techniques developed above to study curves, focusing on curves from genus 0 to genus 6.