相关论文: BPS invariants of semi-stable sheaves on rational …

Using the degeneration formula and absolute/relative correspondence, one studied the change of Gromov-Witten invariants under blow-up for six dimensional symplectic manifolds and obtained closed blow-up formulae for high genus Gromov-Witten…

Let $S$ be a projective simply connected complex surface and $\mathcal{L}$ be a line bundle on $S$. We study the moduli space of stable compactly supported 2-dimensional sheaves on the total spaces of $\mathcal{L}$. The moduli space admits…

Motivated by the counting of BPS states in string theory with orientifolds, we study moduli spaces of self-dual representations of a quiver with contravariant involution. We develop Hall module techniques to compute the number of points…

We generalize the geometrical formulation of Wilson loops recently introduced in arXiv:2003.01729v2 to the description of Wilson Surfaces. For N=(2,0) theory in six dimensions, we provide an explicit derivation of BPS Wilson Surfaces with…

The hydrodynamic stability behaviour of a two-layer falling film is explored with a floating flexible plate on the top surface. The stress balance at the surface is modeled using a modified membrane equation. There is an insoluble…

Exact BPS solutions of multi-walls are obtained in five-dimensional supergravity. The solutions contain 2n parameters similarly to the moduli space of the corresponding global SUSY models and have a smooth limit of vanishing gravitational…

Motivated by S-duality modularity conjectures in string theory, we study the Donaldson-Thomas type invariants of pure 2-dimensional sheaves inside a nonsingular threefold X in three different situations: (1). X is a K3 fibration over a…

Using the degeneration technique, one studies the behavior of Welschinger invariants under the blow-up, and obtains some blow-up formulae of Welschinger invariants. One also analyses the variation of Welschinger invariants when replacing a…

The Bounded Negativity Conjecture predicts that for every complex projective surface $X$ there exists a number $b(X)$ such that $C^2\geq -b(X)$ holds for all reduced curves $C\subset X$. For birational surfaces $f:Y\to X$ there have been…

New birational invariants for a projective manifold are defined by using Lawson homology. These invariants can be highly nontrivial even for projective threefolds. Our techniques involve the weak factorization theorem of Wlodarczyk and…

We study three instability stratifications of the stack of twisted Higgs bundle of a fixed rank and degree on a smooth complex projective curve. The first is the Harder-Narasimhan (HN) stratification, defined by the instability type of the…

The linear dynamics and instability mechanisms of double-layered weakly viscoelastic fluid flowing over an inclined plane are analyzed in the presence of insoluble surfactant at both the free surface and interface. The constitutive equation…

In this note we study refined BPS invariants associated with certain quantum line defects in quantum field theories of class $\mathcal{S}$. Such defects can be specified via geometric engineering in the UV by assigning a path on a certain…

All high-temperature phases of the known N=4 superstrings in five dimensions can be described by the universal thermal potential of an effective four-dimensional supergravity. This theory, in addition to three moduli s, t, u, contains…

A method is given for generating a bounded invariant of a differential system with a given set of initial conditions around a point $x_0$. This invariant has the form of a tube centered on the Euler approximate solution starting at $x_0$,…

In alignment with a programme by Donaldson and Thomas [DT], Thomas [Th] constructed a deformation invariant for smooth projective Calabi-Yau threefolds, which is now called the Donaldson-Thomas invariant, from the moduli space of…

We consider a rational map f:S->S of a complex projective surface together with an invariant meromorphic two form. Under a mild topological assumption on the map, we show that the zeroes of the invariant form can be eliminated by birational…

The space of smooth rational cubic curves in projective space $\PP^r$ ($r\ge 3$) is a smooth quasi-projective variety, which gives us an open subset of the corresponding Hilbert scheme, the moduli space of stable maps, or the moduli space…

This paper deals with a kind of design of a ruled surface. It combines concepts from the fields of computer aided geometric design and kinematics. A dual unit spherical B\'ezier-like curve on the dual unit sphere (DUS) is obtained with…

We apply the wall crossing structure formalism of Kontsevich and Soibelman to Seiberg-Witten integrable systems associated to pure $SU(3)$. This gives an algorithm for computing the Donaldson-Thomas invariants, which correspond to BPS…