[pbelmans]

Stacked on #30, with feat/global-generation as the base branch. This PR has no dependency on #26 (Künneth bundle cohomology).

Degeneracy loci with nonconstant source bundles require relative Grassmann incidence spaces. This adds their bundle operations and fibrewise Borel–Weil–Bott calculations, retaining filtrations and symbolic ranks of induced maps.

• Expose AmbientBundle <: Bundle for completely reducible and filtered homogeneous bundles.
• Add Schur functors for completely reducible and filtered bundles.
• Use GrassmannBundle(1, E) for projective bundles through one relative implementation.
• Add relative zero-locus cohomology, Hodge, polyvector and degree calculations.
• Add determinantal, arbitrary-corank Pfaffian, symmetric and the two supported orbital constructions, plus Eagon–Northcott, Buchsbaum–Rim, Gulliksen–Negard and Buchsbaum–Eisenbud resolutions.
• Introduce DegeneracyLocus and DegeneracyLocusBundle, with explicit incidence_resolution access, opt-in generation/smoothness/nonemptiness checks, and an is_strongly_fano positivity query.

The constructors assume a general section, regularity and expected dimension. When the deeper-stratum bound does not identify the image with its incidence resolution, cohomological calculations refer to the resolution. Positivity checks are sufficient certificates. The optional generation checks reuse #30’s API.

Homogeneous and relative zero-locus presentations share the kernel/cokernel solver. Relative cohomology uses one Leray implementation, and Schur determinants accumulate tensor multiplicities directly.

All tests remain in test/runtests.jl. There is no IntersectionTheory or Oscar dependency.

Validation on Julia 1.13:

• Full suite: 2,318 assertions passed.
• Doctests and the full documentation build passed.
• All 44 tracked Julia files pass JuliaFormatter 2.9.3.
• No method ambiguities involving the new APIs.
• Product, projective-space and conic controls cover relative arithmetic, dictionary/display, normal/conormal and Hochschild APIs.
• Relative BWB agrees with homogeneous products and Serre duality; filtered Schur functors agree with exterior and symmetric powers. Larger Schur determinants agree with independent GL(6) Weyl dimensions.
• Exact presentations of rank-zero relative bundles are recognized as zero, including through the degeneracy wrapper.

Draft review focus: relative BWB and filtration handling, the image/resolution API boundary, and the conservative geometry certificates. The supported-version and platform matrix remains for CI.

[codecov]

Codecov Report

❌ Patch coverage is 99.70845% with 2 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
src/DegeneracyLoci.jl	99.64%	1 Missing ⚠️
src/RelativeZeroLoci.jl	99.39%	1 Missing ⚠️

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