Anomaly equations and intersection theory
DS Park - Journal of High Energy Physics, 2012 - Springer
A bstract Six-dimensional supergravity theories with\(\mathcal {N}\)=(1, 0) supersymmetry
must satisfy anomaly equations. These equations come from demanding the cancellation of …
must satisfy anomaly equations. These equations come from demanding the cancellation of …
Euler characteristics of crepant resolutions of Weierstrass models
M Esole, P Jefferson, MJ Kang - Communications in Mathematical Physics, 2019 - Springer
Based on an identity of Jacobi, we prove a simple formula that computes the pushforward of
analytic functions of the exceptional divisor of a blowup of a projective variety along a …
analytic functions of the exceptional divisor of a blowup of a projective variety along a …
The Geometry of the SU (2)× G2-model
M Esole, MJ Kang - Journal of High Energy Physics, 2019 - Springer
A bstract We study elliptic fibrations that geometrically engineer an SU (2)× G 2 gauge
theory realized by a Weierstrass model for the collision III+ I* ns 0. We find all the distinct …
theory realized by a Weierstrass model for the collision III+ I* ns 0. We find all the distinct …
The Geometry of F-Models
M Esole, P Jefferson, MJ Kang - arXiv preprint arXiv:1704.08251, 2017 - arxiv.org
We study the geometry of elliptic fibrations satisfying the conditions of Step 8 of Tate's
algorithm. We call such geometries F $ _4 $-models, as the dual graph of their special fiber …
algorithm. We call such geometries F $ _4 $-models, as the dual graph of their special fiber …
The Geometry of G, Spin(7), and Spin(8)-models
M Esole, R Jagadeesan, MJ Kang - arXiv preprint arXiv:1709.04913, 2017 - arxiv.org
We study the geometry of elliptic fibrations given by Weierstrass models resulting from Step
6 of Tate's algorithm. Such elliptic fibrations have a discriminant locus containing an …
6 of Tate's algorithm. Such elliptic fibrations have a discriminant locus containing an …
Mordell-Weil torsion, anomalies, and phase transitions
M Esole, MJ Kang, ST Yau - arXiv preprint arXiv:1712.02337, 2017 - arxiv.org
We explore how introducing a non-trivial Mordell-Weil group changes the structure of the
Coulomb phases of a five-dimensional gauge theory from an M-theory compactified on an …
Coulomb phases of a five-dimensional gauge theory from an M-theory compactified on an …
D5 elliptic fibrations: non-Kodaira fibers and new orientifold limits of F-theory
M Esole, J Fullwood, ST Yau - arXiv preprint arXiv:1110.6177, 2011 - arxiv.org
A D5 elliptic fibration is a fibration whose generic fiber is modeled by the complete
intersection of two quadric surfaces in P3. They provide simple examples of elliptic fibrations …
intersection of two quadric surfaces in P3. They provide simple examples of elliptic fibrations …
Flopping and slicing: SO (4) and Spin (4)-models
M Esole, MJ Kang - arXiv preprint arXiv:1802.04802, 2018 - arxiv.org
We study the geometric engineering of gauge theories with gauge group Spin (4) and SO (4)
using crepant resolutions of Weierstrass models. The corresponding elliptic fibrations realize …
using crepant resolutions of Weierstrass models. The corresponding elliptic fibrations realize …
[PDF][PDF] 48 crepant paths to SU (2)× SU (3)
M Esole, R Jagadeesan, MJ Kang - arXiv preprint arXiv:1905.05174, 2019 - academia.edu
We study crepant resolutions of Weierstrass models of SU (2)× SU (3)-models, whose gauge
group describes the non-abelian sector of the Standard Model. The SU (2)× SU (3)-models …
group describes the non-abelian sector of the Standard Model. The SU (2)× SU (3)-models …
Stable pairs and the HOMFLY polynomial
D Maulik - Inventiones mathematicae, 2016 - Springer
Given a planar curve singularity, we prove a conjecture of Oblomkov–Shende, relating the
geometry of its Hilbert scheme of points to the HOMFLY polynomial of the associated …
geometry of its Hilbert scheme of points to the HOMFLY polynomial of the associated …