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Filtrations on Combinatorial Intersection Cohomology and Invariants of Subdivisions

Tsang, Ling Hei
http://rave.ohiolink.edu/etdc/view?acc_num=osu16696323357962

Abstract Details

2022, Doctor of Philosophy, Ohio State University, Mathematics.
Motivated by definitions in mixed Hodge theory, we define the weight filtration and the monodromy weight filtration on the combinatorial intersection cohomology of a fan. These filtrations give a natural definition of some multivariable invariants of subdivisions of polytopes, lattice polytopes, and fans, namely, the mixed h-polynomial, the refined limit mixed h*-polynomial and the mixed cd-index. Previously, only the refined limit mixed h*-polynomial had a geometric interpretation, which came from filtrations on the cohomology of a schön hypersurface. In addition, using comodule techniques, we show that the mixed cd-index determines the mixed h-polynomial.
Eric Katz (Advisor)
David Anderson (Committee Member)
Maria Angelica Cueto (Committee Member)
134 p.
Mathematics
Fan subdivisions; toric h-polynomial; h*-polynomial; cd-index; filtrations

Recommended Citations

Citations

  • Tsang, L. H. (2022). Filtrations on Combinatorial Intersection Cohomology and Invariants of Subdivisions [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu16696323357962

    APA Style (7th edition)

  • Tsang, Ling Hei. Filtrations on Combinatorial Intersection Cohomology and Invariants of Subdivisions. 2022. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu16696323357962.

    MLA Style (8th edition)

  • Tsang, Ling Hei. "Filtrations on Combinatorial Intersection Cohomology and Invariants of Subdivisions." Doctoral dissertation, Ohio State University, 2022. http://rave.ohiolink.edu/etdc/view?acc_num=osu16696323357962

    Chicago Manual of Style (17th edition)

osu16696323357962
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