From 3f4c2c70a4b91659c778d46cfd6ceb6f891bdef9 Mon Sep 17 00:00:00 2001
From: Rohan <rohanjoshi.berkeley.edu>
Date: Tue, 4 Jun 2024 16:35:06 -0600
Subject: [PATCH] Added Fano examples to tests

---
 ToricExtras.m2                      |  5 ++-
 ToricExtras/BatyrevConstructions.m2 | 34 ++++++++++++++++
 ToricExtras/BatyrevTests.m2         | 60 ++++++++++++++++++++++++++---
 3 files changed, 93 insertions(+), 6 deletions(-)

diff --git a/ToricExtras.m2 b/ToricExtras.m2
index 475abe2..9fb659d 100644
--- a/ToricExtras.m2
+++ b/ToricExtras.m2
@@ -61,7 +61,10 @@ newPackage(
 	{
             Name => "Will Gilroy",
             Email => "wlg38@cornell.edu"
-	}
+	},
+        {
+	    Name => "Rohan Joshi",
+	    Email => "rohansjoshi@math.ucla.edu"}
         },
 
     Headline => "new routines for working with normal toric varieties",
diff --git a/ToricExtras/BatyrevConstructions.m2 b/ToricExtras/BatyrevConstructions.m2
index 9516e82..b5b8a9a 100644
--- a/ToricExtras/BatyrevConstructions.m2
+++ b/ToricExtras/BatyrevConstructions.m2
@@ -90,3 +90,37 @@ batyrevConstructor(List, List, List) := (P, B, C) -> (
 )
 
 
+end-------
+
+degreeOfThreefold = method();
+degreeOfThreefold(NormalToricVariety) := X -> (
+    K = toricDivisor X;
+    c = chern(1, OO (-K)); -- anticanonical class in the Chow ring
+    deg = integral (c*c*c);
+    -- g = 1 + (deg / 2)
+    return deg;
+    
+    
+
+    
+-- There are 7 smooth Fano 3-folds of Picard rank 3. Of these 5 are projectivations of direct sums of two line bundles over surfaces of Picard rank 2, and by Batyrev's paper have 3 primitive collections
+-- Therefore, the remaining two (3-26) and (3-29) have Picard rank 
+
+load "BatyrevConstructions.m2"
+
+X = batyrevConstructor({2,1,1,1,1}, {-2}, {})
+--X = toricProjectiveSpace 3
+K = toricDivisor X
+c = chern(1, OO (-K))
+deg = integral (c*c*c)
+--g = 1 + (deg / 2)
+
+X = batyrevConstructor({1,1,1,1,1}, {2}, {})
+
+integral (c*c*c)
+
+isFano X
+isSmooth X
+isProjective X
+isNef(-toricDivisor X)
+isAmple(-toricDivisor X)
diff --git a/ToricExtras/BatyrevTests.m2 b/ToricExtras/BatyrevTests.m2
index 8a2b7fb..1702834 100644
--- a/ToricExtras/BatyrevTests.m2
+++ b/ToricExtras/BatyrevTests.m2
@@ -1,31 +1,81 @@
 TEST ///
 -- a 2-dimensional fan where the partition sizes of the primitive collections are equal
+-- This constructs the unique smooth toric del Pezzo surface of Picard rank 3, which is the Bl_1(P^1 x P^1) = Bl_2(P^2)
 V = batyrevConstructor({1,1,1,1,1}, {0}, {})
 assert(isWellDefined V)
 assert(isSmooth V)
 assert(isProjective V)
 assert(rank picardGroup V == 3)
+assert(isFano(V))
 ///
+TEST ///
+-- This constructs a smooth toric weak del Pezzo surface of Picard rank 3, which is the blowup of Bl_1 P^2 at the torus fixed-point on the exceptional divisor
+V = batyrevConstructor({1,1,1,1,1}, {1}, {})
+assert(isWellDefined V)
+assert(isSmooth V)
+assert(isProjective V)
+assert(rank picardGroup V == 3)
+assert(not isFano(V)) -- not Fano
+assert(isNef(-toricDivisor V)) -- but it is weak Fano
 
+///
 TEST ///
--- a 3-dimensional fan where the partition sizes of the primitive collections are not the same
-V = batyrevConstructor({1,1,1,2,1},{0,0},{})
+-- This constructs a smooth toric Fano of Picard rank 3 which is 3-26 on Fanography. It can be described as the blowup of P^3 at the disjoint union of a point and a line
+V = batyrevConstructor({2,1,1,1,1}, {0}, {})
 assert(isWellDefined V)
 assert(isSmooth V)
 assert(isProjective V)
 assert(rank picardGroup V == 3)
+assert(isFano(V))
+
+degreeOfThreefold = X -> (
+    K := toricDivisor X;
+    c := chern(1, OO (-K));
+    integral (c*c*c)
+)
+
+assert(degreeOfThreefold(V) == 46)
+
+///
+TEST ///
+-- This constructs a smooth toric Fano of Picard rank 3 which is 3-29 on Fanography. It can be described as the blowup of Bl_1 P^3 along a line in the exceptional divisor
+V = batyrevConstructor({2,1,1,1,1}, {1}, {})
+assert(isWellDefined V)
+assert(isSmooth V)
+assert(isProjective V)
+assert(rank picardGroup V == 3)
+assert(isFano(V))
+
+degreeOfThreefold = X -> (
+    K := toricDivisor X;
+    c := chern(1, OO (-K));
+    integral (c*c*c)
+)
+
+assert(degreeOfThreefold(V) == 50)
+
 ///
 
 TEST ///
--- a 12-dimensional fan where the partition sizes of the primitive collection are all different
--- 15 rays with 105 maximal cones
-V = batyrevConstructor({1,2,3,4,5},{0,0,0,0},{0,0})
+-- a 3-dimensional fan where the partition sizes of the primitive collections are not the same
+V = batyrevConstructor({1,1,1,2,1},{0,0},{})
 assert(isWellDefined V)
 assert(isSmooth V)
 assert(isProjective V)
 assert(rank picardGroup V == 3)
 ///
 
+-- GOOD TEST BUT TAKES TOO LONG:
+--TEST ///
+-- a 12-dimensional fan where the partition sizes of the primitive collection are all different
+-- 15 rays with 105 maximal cones
+--V = batyrevConstructor({1,2,3,4,5},{0,0,0,0},{0,0})
+--assert(isWellDefined V)
+--assert(isSmooth V)
+--assert(isProjective V)
+--assert(rank picardGroup V == 3)
+--///
+