The authors build a resolution stack for the KSBA-K-moduli wall crossing of plane quartics and compute its Chow ring and cohomology with rational coefficients.
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The authors define divisible weighted projective spaces, give sharp bounds for minimal-degree non-degenerate subvarieties therein, and develop a theory of weighted determinantal scrolls that achieve minimal degree while satisfying weighted N_p properties tied to regularity notions.
For smooth projective X of dim d≥5, D^b(X^[3]) admits a semi-orthogonal sequence of length binom(d-3,2) with each term equivalent to D(X) via FM transform from a Grassmannian bundle G over X.
Proves existence of positive-density hypersurfaces over finite fields intersecting a reduced equidimensional quasiprojective scheme X such that multiplicity e_P is preserved at all closed points P of the intersection.
The integral Chow ring of M_0(P^r, 2) is presented as a quotient of a three-variable polynomial ring with all non-trivial relations encoded by two rational generating functions.
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Chow and cohomology rings of moduli stacks of plane quartics
The authors build a resolution stack for the KSBA-K-moduli wall crossing of plane quartics and compute its Chow ring and cohomology with rational coefficients.
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Varieties of minimal degree in weighted projective space
The authors define divisible weighted projective spaces, give sharp bounds for minimal-degree non-degenerate subvarieties therein, and develop a theory of weighted determinantal scrolls that achieve minimal degree while satisfying weighted N_p properties tied to regularity notions.
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A Semi-orthogonal Sequence in the Derived Category of the Hilbert Scheme of Three Points
For smooth projective X of dim d≥5, D^b(X^[3]) admits a semi-orthogonal sequence of length binom(d-3,2) with each term equivalent to D(X) via FM transform from a Grassmannian bundle G over X.
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Bertini theorems for Hilbert-Samuel multiplicity over finite fields
Proves existence of positive-density hypersurfaces over finite fields intersecting a reduced equidimensional quasiprojective scheme X such that multiplicity e_P is preserved at all closed points P of the intersection.
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The integral Chow ring of $\mathscr{M}_{0}(\mathbb{P}^r, 2)$
The integral Chow ring of M_0(P^r, 2) is presented as a quotient of a three-variable polynomial ring with all non-trivial relations encoded by two rational generating functions.