post 17 fix

docs/_posts/2024-3-13-enumgeo.md

@@ -1,6 +1,6 @@
 ---
 layout: post
-date: 2024-4-8
+date: 2024-7-22
 title: "Post 17: A Taste of Enumerative Geometry"
 permalink: /post17.html
 katex: true
@@ -121,9 +121,19 @@ This formula applies to both $C$ and $L$. The genus of a line is $0$. Furthermor
 
 The third equation is obtained by multiplying $[C]_S + [L]_S = t\sigma$ by $[C]_S$ and $[L]_S$ separately. We see that we can use $\deg([L]_S^2)=\deg([C]_S^2)-t(st-2)$ in the second equation to solve for $\deg([C]_S^2)$, and then use it in the first equation to solve for $g$. Indeed, we get:
 
-$$0 = \deg([C]_S^2) - t(st-2) + s-4 + 2,$$ so
-$$\deg([C]_S^2) = t(st-2)+2-s,$$ so
-$$g = t(st-2)/2 + 1 -s/2 + (s-4)(st-1)/2 + 1$$ $$= t(st-2)/2 - (s-4)/2 + (s-4)(st-1)/2$$ $$= (s+t-4)(st-2)/2.$$
+$$0 = \deg([C]_S^2) - t(st-2) + s-4 + 2,$$
+
+so
+
+$$\deg([C]_S^2) = t(st-2)+2-s,$$
+
+so
+
+$$g = t(st-2)/2 + 1 -s/2 + (s-4)(st-1)/2 + 1$$
+
+$$= t(st-2)/2 - (s-4)/2 + (s-4)(st-1)/2$$
+
+$$= (s+t-4)(st-2)/2.$$
 
 # Conclusion