Open Access. Powered by Scholars. Published by Universities.®
- Publication Type
Articles 1 - 2 of 2
Full-Text Articles in Algebraic Geometry
Tropical Derivation Of Cohomology Ring Of Heavy/Light Hassett Spaces, Shiyue Li
Tropical Derivation Of Cohomology Ring Of Heavy/Light Hassett Spaces, Shiyue Li
HMC Senior Theses
The cohomology of moduli spaces of curves has been extensively studied in classical algebraic geometry. The emergent field of tropical geometry gives new views and combinatorial tools for treating these classical problems. In particular, we study the cohomology of heavy/light Hassett spaces, moduli spaces of heavy/light weighted stable curves, denoted as $\calm_{g, w}$ for a particular genus $g$ and a weight vector $w \in (0, 1]^n$ using tropical geometry. We survey and build on the work of \citet{Cavalieri2014}, which proved that tropical compactification is a \textit{wonderful} compactification of the complement of hyperplane arrangement for these heavy/light Hassett spaces. For $g …
Strong Nonnegativity And Sums Of Squares On Real Varieties, Mohamed Omar, Brian Osserman
Strong Nonnegativity And Sums Of Squares On Real Varieties, Mohamed Omar, Brian Osserman
All HMC Faculty Publications and Research
Motivated by scheme theory, we introduce strong nonnegativity on real varieties, which has the property that a sum of squares is strongly nonnegative. We show that this algebraic property is equivalent to nonnegativity for nonsingular real varieties. Moreover, for singular varieties, we reprove and generalize obstructions of Gouveia and Netzer to the convergence of the theta body hierarchy of convex bodies approximating the convex hull of a real variety.