Update SpecialFanoFourfolds by giovannistagliano · Pull Request #4665 · Macaulay2/M2

giovannistagliano · 2026-08-25T10:19:02Z

No description provided.

d-torrance

Thanks for the update!

I have a few comments. Also, should the new features be documented?

d-torrance · 2026-08-26T11:03:11Z

 );

+-- consider implementing image(MultihomogeneousRationalMap,String) in Cremona.m2
+image (WeightedRationalMap,String) := (Phi,alg) -> (


Should this new method be documented?

Also, should the MultiprojectiveVarieties package also get a version bump since it's getting this new method?

Actually, this is a very minor update. The functionality is already documented via image(MultirationalMap, String). This change simply avoids a "not implemented yet" error by automatically redirecting the call to the existing implementation.

d-torrance · 2026-08-26T11:09:00Z

+        local L; local C;
+        if member(recognizeDSCF X, {"DSCF-V1-31", "DSCF-V1-34"}) then (
+            -- last(U.cache#"exceptionalCurves") determines a conic curve on the surface U'' corresponding to another fourfold X''
+            assert(U.cache#?"special curves on U" and #(U.cache#"special curves on U") == 1);


I'd recommend calling error with an informative error messages so we don't just get a cryptic "assertion failed" message:

Suggested change

assert(U.cache#?"special curves on U" and #(U.cache#"special curves on U") == 1);

if not U.cache#?"special curves on U" or #(U.cache#"special curves on U") != 1

then error "informative error message";

Same comment for the other assert statements below.

I replaced a few asserts with informative error messages. The remaining ones are just sanity checks for situations that should never occur, so users should never see those messages.

d-torrance · 2026-08-26T11:12:09Z

+    if o.Verbose then << "-- upper bound for the dimension of the family of reducible surfaces S ∪ P in X: " << dimFamReducSurfInX << endl;
+    z := 54 - (dimFamReducSurf + b - dimFamReducSurfInX);
+    if o.Verbose then << "-- codim. in C_8 of {[X] : S ∪ P ⊂ X} ≤ " << 54 << " - (" << dimFamReducSurf + b << " - " << dimFamReducSurfInX << ") = " << z << emo(z == 1) << endl;
+    return X.cache#(S,P,"parameterCount") = (z, (b+1, dimFamReducSurf, dimFamReducSurfInX));


return isn't necessary on the last line of a function (if you remove the ;)

d-torrance · 2026-08-26T11:21:42Z

+    if isFanoMapStandard X and recognizeDSCF X === "DSCF-V1-20" then return (true, (sectionalGenus U)+2);
+    << "-- warning: expected invariants of the K3 surface unavailable; unverified values may be used" << endl;
+    if isFanoMapStandard X and member(recognizeDSCF X,{"DSCF-V1-5","DSCF-V1-14"}) then return (false, (sectionalGenus U)+1);
+    if isFanoMapStandard X and recognizeDSCF X === "DSCF-V1-16" then (false, sectionalGenus U);


The DSCF-V1-16 case is getting skipped with no return:

Suggested change

if isFanoMapStandard X and recognizeDSCF X === "DSCF-V1-16" then (false, sectionalGenus U);

if isFanoMapStandard X and recognizeDSCF X === "DSCF-V1-16" then return (false, sectionalGenus U);

d-torrance · 2026-08-26T11:49:41Z

+    G := groebnerBasis(V,Strategy=>alg);
+    G' := ideal sub(selectInSubring(1,G),K[x_0..x_m]);
+    Z := projectiveVariety(sub(G',vars ring ambient target Phi),MinimalGenerators=>false,Saturate=>false);
+    forceImage(Phi,Z);


I'm getting an error here with this example (discovered by Claude):

i3 : kk = ZZ/101; Q = PP_kk^4; P = PP_kk(1, 1, 1, 3); R = ring Q; o4 : ProjectiveVariety, PP^4 o5 : ProjectiveVariety, PP(1,1,1,3) i7 : phi = (Hom(Q, P)) {random(R^1, R^{-1,-1,-1,-3})}; o7 : WeightedRationalMap (rational map from Q to P) i8 : image(phi, "F4") ../../../../M2/M2/Macaulay2/packages/MultiprojectiveVarieties.m2:1599:10:(2):[3]: error: assertion failed ../../../../M2/M2/Macaulay2/packages/MultiprojectiveVarieties.m2:1599:10:(2): entering debugger (enter 'help' to see commands) ../../../../M2/M2/Macaulay2/packages/MultiprojectiveVarieties.m2:1599:4-1599:53: --source code: assert(Phi#"image" =!= null and Phi#"image" == X); ii9 : Phi#"image" === null oo9 = true

Thanks for the example. I've fixed it.

d-torrance · 2026-08-26T11:55:29Z

+    (mu,U,exC,f) := building Utilde;
+    (L,C) := toSequence exC;
+    X := recoverFourfold Utilde;
+    (woWarn,g') := unverifiedExpectedGenusOfK3FromExceptionalCurves(X,U,L,C);


It would be good to only run these computations if we're using one of the two new strategies

d-torrance · 2026-08-26T12:01:09Z

+
+building EmbeddedK3SurfaceFromDoublySpecialCubicFourfold := E -> (
+    (mu,U,LC,f) := building E#"ParentK3Surface";
+    (mu,U,LC,toSequence prepend(f,E#"MapFromParentK3Surface"))


The other building methods all return a sequence whose 4th element is a rational map. Maybe it would be good to have another way to get this map from the parent surface for consistency?

I see the consistency issue. However, for this subtype, the 4th component would be the composition of all those rational maps, so achieving the same consistency would require additional computation. Also, building is mainly intended for internal use.

d-torrance · 2026-08-26T12:03:36Z

+recoverFourfold EmbeddedK3SurfaceFromDoublySpecialCubicFourfold := E -> recoverFourfold E#"ParentK3Surface";
+
+K3SurfaceFromDoublySpecialCubicFourfold Sequence := (E,ab) -> (
+    Verb := true;


Is thie Verb := true still supposed to be here? It looks like maybe an artifact from debugging the code

d-torrance · 2026-08-26T12:03:53Z

+        if degree D != a*M_(0,1) + b*M_(1,1) then error "failed to obtain polarization: divisor curve has unexpected degree";
+        A = matrix {{2*g-2, degree D}, {degree D, M_(1,1)}};
+    );
+    if det A != det M then << ("-- incorrect lattice discriminant on the genus "|(toString g)|" K3 surface: "|(toString det A)) << endl;


Should this be an error?

d-torrance · 2026-08-26T12:14:52Z

+    S := L#"UnderlyingSurface";
+    H := S * random(1,0_S);
+    C := L#"specialCurve";
+    assert(dim H == 1 and dim C == 1);


A more descriptive error message would be good here rather than assert. Also, what if C is null? Claude found the following example:

i2 : X = specialFourfold surface((2,0,0),(1,0,0),ZZ/61001); o2 : ProjectiveVariety, cubic fourfold in C_8 containing a surface of degree 4 and sectional genus 0 and a plane i3 : T = polarizedK3surface polarizedK3surface(X,Verbose=>false); o3 : Lattice-polarized K3 surface associated to X — K3 status: [▓▓▓▓▓ / ▓▓▓▓▓] i4 : T' = polarizedK3surface(T,Strategy=>"MapFromU-Virtual",Verbose=>false); o4 : Lattice-polarized K3 surface associated to X — K3 status: [▓▓▓▓░ / ▓▓▓▓▓] i5 : L = T'(1,1); -- (▫) constructing K3 surface of genus 12 in PP^12 -- using divisor D = aH+bC, with D^2=22=2*12-2, where (a,b) = (1,1) -- warning: lattice polarization is virtual; rerun polarizedK3surface with an appropriate option, e.g. Strategy=>"SpecialCurve" o5 : Virtual lattice-polarization on K3 surface associated to X i6 : basis L stdio:6:5:(3):[1]: error: no method found for applying dim to: argument : null (of class Nothing)

giovannistagliano · 2026-08-26T12:48:35Z

Thank you for the many suggestions. I'll address them soon.

giovannistagliano · 2026-08-26T20:28:07Z

I think I've addressed all or almost all of the requested changes. Thanks a lot for the comments. I might still make a few small updates over the next few days.

giovannistagliano added 2 commits August 25, 2026 12:07

minor update to MultiprojectiveVarieties

6f40497

update aux files

be2bda2

d-torrance added the update to existing package(s) label Aug 25, 2026

d-torrance requested review from andrew-tawfeek and d-torrance August 25, 2026 22:22

d-torrance requested changes Aug 26, 2026

View reviewed changes

giovannistagliano added 2 commits August 26, 2026 14:40

minor update

d2c931a

date update

18aa7bd

giovannistagliano added 2 commits August 26, 2026 22:12

minor update

0720e94

address review comments

db07578

	assert(U.cache#?"special curves on U" and #(U.cache#"special curves on U") == 1);
	if not U.cache#?"special curves on U" or #(U.cache#"special curves on U") != 1
	then error "informative error message";

	if isFanoMapStandard X and recognizeDSCF X === "DSCF-V1-16" then (false, sectionalGenus U);
	if isFanoMapStandard X and recognizeDSCF X === "DSCF-V1-16" then return (false, sectionalGenus U);

Uh oh!

Conversation

giovannistagliano commented Aug 25, 2026

Uh oh!

d-torrance left a comment • edited Loading Uh oh! There was an error while loading. Please reload this page.

Uh oh!

Choose a reason for hiding this comment

Uh oh!

Choose a reason for hiding this comment

Uh oh!

Choose a reason for hiding this comment

Uh oh!

Choose a reason for hiding this comment

Uh oh!

Choose a reason for hiding this comment

Uh oh!

Choose a reason for hiding this comment

Uh oh!

Choose a reason for hiding this comment

Uh oh!

Choose a reason for hiding this comment

Uh oh!

Choose a reason for hiding this comment

Uh oh!

Choose a reason for hiding this comment

Uh oh!

Choose a reason for hiding this comment

Uh oh!

Choose a reason for hiding this comment

Uh oh!

Choose a reason for hiding this comment

Uh oh!

Choose a reason for hiding this comment

Uh oh!

Choose a reason for hiding this comment

Uh oh!

giovannistagliano commented Aug 26, 2026

Uh oh!

giovannistagliano commented Aug 26, 2026

Uh oh!

Reviewers

Assignees

Labels

Projects

Milestone

Development

Uh oh!

2 participants

d-torrance left a comment •

edited

Loading